Étude des coefficients de Fourier des fonctions de $L^p(G)$

Bonami, Aline

doi:10.5802/aif.357

Étude des coefficients de Fourier des fonctions de

L^{p} (G)

Bonami, Aline

Annales de l'Institut Fourier, Tome 20 (1970) no. 2, pp. 335-402.

Résumé
Abstract

On étudie la décroissance à l’infini des coefficients de Fourier des fonctions $2 π$ -périodiques intégrables. Soit en particulier $λ_{n}$ une suite lacunaire d’entiers : $λ_{n + 1} \geq 3 λ_{n}$ . On appelle suite $k$ -lacunaire associée la suite $μ_{N}^{k}$ des entiers qui s’écrivent sous la forme $\pm λ_{n_{1}} \pm λ_{n_{2}} \pm \dots \pm λ_{n_{k}}$ , $n_{1} > n_{2} > \dots > n_{k}$ . On montre que si $\int_{0}^{2 π} | f | ({Log}^{+} | f |)^{k / 2} d x$ est fini, il en est de même de $\sum_{N} | \hat{f} (μ_{N}^{k}) |^{2}$ . D’autre part, si $λ_{n}$ satisfait à une condition plus restrictive, quel que soit $1 < p \leq 2$ , si $\int_{0}^{2 π} | f |^{p} d x$ est fini il en est de même de $\sum_{k} (p - 1) \sum_{N} | \hat{f} (μ_{N}^{k}) |^{2}$ . Ces résultats sont généralisés à d’autres groupes que $R / 2 π Z$ , et à d’autres situations. On montre enfin une dernière propriété des séries $k$ -lacunaires : toute série $k$ -lacunaire qui converge sur un ensemble de mesure positive est la série de Fourier d’une fonction de carré sommable.

We study the decrease at infinity of the Fourier coefficients of $2 π$ -periodic integrable functions. Let $λ_{n}$ be a lacunary sequence of integers: $λ_{n + 1} \geq 3 λ_{n}$ : the associated $k$ -lacunary sequence is defined to be the sequence $μ_{N}^{k}$ of integers which can be written as $\pm λ_{n_{1}} \pm λ_{n_{2}} \pm \dots \pm λ_{n_{k}}$ , $n_{1} > n_{2} > \dots > n_{k}$ . It is shown that if $\int_{0}^{2 π} | f | ({Log}^{+} | f |)^{k / 2} d x$ is finite, then $\sum_{N} | \hat{f} (μ_{N}^{k}) |^{2}$ is finite. If $λ_{n}$ satisfies a more restrictive condition, then for every $p$ , $1 < p \leq 2$ , it is shown that if $\int_{0}^{2 π} | f |^{p} d x$ is finite, then $\sum_{k} (p - 1) \sum_{N} | \hat{f} (μ_{N}^{k}) |^{2}$ is finite. These results are generalized to other groups besides $R / 2 π Z$ , and to other situations. It is also shown that every $k$ lacunary sequence which converges in a set of positive measure is the Fourier series of a square summable function.

MR Zbl | 13 citations dans Numdam

DOI : 10.5802/aif.357

@article{AIF_1970__20_2_335_0,
     author = {Bonami, Aline},
     title = {\'Etude des coefficients de {Fourier} des fonctions de $L^p(G)$},
     journal = {Annales de l'Institut Fourier},
     pages = {335--402},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {20},
     number = {2},
     year = {1970},
     doi = {10.5802/aif.357},
     mrnumber = {44 #727},
     zbl = {0195.42501},
     language = {fr},
     url = {https://www.numdam.org/articles/10.5802/aif.357/}
}

TY  - JOUR
AU  - Bonami, Aline
TI  - Étude des coefficients de Fourier des fonctions de $L^p(G)$
JO  - Annales de l'Institut Fourier
PY  - 1970
SP  - 335
EP  - 402
VL  - 20
IS  - 2
PB  - Institut Fourier
PP  - Grenoble
UR  - https://www.numdam.org/articles/10.5802/aif.357/
DO  - 10.5802/aif.357
LA  - fr
ID  - AIF_1970__20_2_335_0
ER  -

%0 Journal Article
%A Bonami, Aline
%T Étude des coefficients de Fourier des fonctions de $L^p(G)$
%J Annales de l'Institut Fourier
%D 1970
%P 335-402
%V 20
%N 2
%I Institut Fourier
%C Grenoble
%U https://www.numdam.org/articles/10.5802/aif.357/
%R 10.5802/aif.357
%G fr
%F AIF_1970__20_2_335_0

Bonami, Aline. Étude des coefficients de Fourier des fonctions de $L^p(G)$. Annales de l'Institut Fourier, Tome 20 (1970) no. 2, pp. 335-402. doi : 10.5802/aif.357. https://www.numdam.org/articles/10.5802/aif.357/

Bibliographie
Cité par

[1] A. Bonami, Ensembles Λ(p) dans le dual de D∞, Ann. Inst. Fourier, tome 18, fascicule 2, p. 193. | Numdam | MR | Zbl

[2] A. Bonami et Y. Meyer, Propriétés de convergence de certaines séries trigonométriques, C.R. Acad. Sc. Paris, tome 269, p. 68. | MR | Zbl

[3] J.-P. Kahane et R. Salem, Ensembles parfaits et séries trigonométriques, Actualités scientifiques et industrielles n° 1301, 1962. | Zbl

[4] Y. Meyer, Endomorphismes des idéaux fermés de L1(G), Classes de Hardy et Séries lacunaires, Ann. Sci. École Norm. Sup., 4e série, tome 1, 1968, p. 499. | Numdam | Zbl

[5] R. Rado, A combinatorial theorem on vector spaces, J. London Math. Soc.. 37, p. 351. | MR | Zbl

[6] W. Rudin, Trigonometric series with gaps, J. of Math. and Mech., 9, p. 203. | MR | Zbl

[7] W. Rudin, Fourier Analysis on groups, Interscience tracts in pure and applied mathematics n° 12, 1962. | MR | Zbl

[8] M. Schreiber, Fermeture en probabilité des chaos de Wiener, C.R. Acad. Sci., tome 265, p. 859. | MR | Zbl

[9] A. Zygmund, Trigonometric series, tome 1, Cambridge University Press, 1959. | Zbl

[10] A. Zygmund, Trigonometric series, tome 2, Cambridge University Press, 1959. | Zbl

Beatty, Emily; Stilck França, Daniel Order p Quantum Wasserstein Distances from Couplings, Annales Henri Poincaré (2025) | DOI:10.1007/s00023-025-01557-z
Mariona, Alexander; Esfahanizadeh, Homa; D'Oliveira, Rafael Gregorio Lucas; Médard, Muriel When Information Is a Function of Data – Some Information Theoretic Perspectives on Semantic Communications, Foundations of Semantic Communication Networks (2025), p. 111 | DOI:10.1002/9781394247912.ch5
Jiao, Yong; Luo, Sijie; Zhou, Dejian Functional L1-L inequalities in the CAR algebra, Journal of Functional Analysis, Volume 288 (2025) no. 2, p. 110700 | DOI:10.1016/j.jfa.2024.110700
Bangachev, Kiril; Bresler, Guy Random Algebraic Graphs and Their Convergence to ErdőS–Rényi, Random Structures Algorithms, Volume 66 (2025) no. 1 | DOI:10.1002/rsa.21276
Arunachalam, Srinivasan; Doriguello, Joao F. Matrix hypercontractivity, streaming algorithms and LDCs: the large alphabet case, ACM Transactions on Computation Theory, Volume 16 (2024) no. 4, p. 1 | DOI:10.1145/3688824
Karagulyan, G.A. Sharp inequalities involving multiplicative chaos sums, Acta Mathematica Hungarica, Volume 173 (2024) no. 2, p. 340 | DOI:10.1007/s10474-024-01451-w
Johnson, W. B.; Schechtman, G. Approximate identities for ideals in L(Lp) $L (L^{p})$ , Bulletin of the London Mathematical Society, Volume 56 (2024) no. 12, p. 3708 | DOI:10.1112/blms.13161
Jiao, Yong; Luo, Sijie; Zanin, Dmitriy; Zhou, Dejian Noncommutative Logarithmic Sobolev Inequalities, Communications in Mathematical Physics, Volume 405 (2024) no. 11 | DOI:10.1007/s00220-024-05145-w
Friedgut, Ehud An Information-Theoretic Proof of a Hypercontractive Inequality, Entropy, Volume 26 (2024) no. 11, p. 966 | DOI:10.3390/e26110966
Yu, Lei; Anantharam, Venkat; Chen, Jun Graphs of Joint Types, Noninteractive Simulation, and Stronger Hypercontractivity, IEEE Transactions on Information Theory, Volume 70 (2024) no. 4, p. 2287 | DOI:10.1109/tit.2024.3357859
Cohen, Guy; Lin, Michael L2-Quasi-compact and hyperbounded Markov operators, Israel Journal of Mathematics, Volume 264 (2024) no. 1, p. 281 | DOI:10.1007/s11856-024-2648-3
Cordero‐Erausquin, Dario; Eskenazis, Alexandros Discrete logarithmic Sobolev inequalities in Banach spaces, Journal of the London Mathematical Society, Volume 109 (2024) no. 2 | DOI:10.1112/jlms.12873
Golovnev, Alexander; Posobin, Gleb; Regev, Oded; Weinstein, Omri Polynomial Data Structure Lower Bounds in the Group Model, SIAM Journal on Computing, Volume 53 (2024) no. 6, p. FOCS20-74 | DOI:10.1137/20m1381988
Cordero-Erausquin, Dario; Eskenazis, Alexandros Talagrand’s influence inequality revisited, Analysis PDE, Volume 16 (2023) no. 2, p. 571 | DOI:10.2140/apde.2023.16.571
Oleszkiewicz, Krzysztof Boolean Functions with Small Second-Order Influences on the Discrete Cube, High Dimensional Probability IX, Volume 80 (2023), p. 155 | DOI:10.1007/978-3-031-26979-0_6
Keevash, Peter; Lifshitz, Noam; Long, Eoin; Minzer, Dor Hypercontractivity for global functions and sharp thresholds, Journal of the American Mathematical Society, Volume 37 (2023) no. 1, p. 245 | DOI:10.1090/jams/1027
Karagulyan, G. A.; Karagulyan, V. G. On Uniqueness Properties of Rademacher Chaos Series, Mathematical Notes, Volume 114 (2023) no. 5-6, p. 1225 | DOI:10.1134/s0001434623110548
Song, Dogyoon; Parrilo, Pablo A. On approximations of the PSD cone by a polynomial number of smaller-sized PSD cones, Mathematical Programming, Volume 198 (2023) no. 1, p. 733 | DOI:10.1007/s10107-022-01795-7
Gozlan, N.; Li, Xue-Mei; Madiman, M.; Roberto, C.; Samson, P.-M. Log-Hessian and Deviation Bounds for Markov Semi-Groups, and Regularization Effect in $L^{1}$ , Potential Analysis, Volume 58 (2023) no. 1, p. 123 | DOI:10.1007/s11118-021-09934-z
Ellis, David; Kindler, Guy; Lifshitz, Noam, Proceedings of the 55th Annual ACM Symposium on Theory of Computing (2023), p. 656 | DOI:10.1145/3564246.3585116
Hayakawa, Satoshi; Oberhauser, Harald; Lyons, Terry Hypercontractivity meets random convex hulls: analysis of randomized multivariate cubatures, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Volume 479 (2023) no. 2273 | DOI:10.1098/rspa.2022.0725
Mei, Song; Misiakiewicz, Theodor; Montanari, Andrea Generalization error of random feature and kernel methods: Hypercontractivity and kernel matrix concentration, Applied and Computational Harmonic Analysis, Volume 59 (2022), p. 3 | DOI:10.1016/j.acha.2021.12.003
Levhari, Niv; Samorodnitsky, Alex Hypercontractive Inequalities for the Second Norm of Highly Concentrated Functions, and Mrs. Gerber’s-Type Inequalities for the Second Rényi Entropy, Entropy, Volume 24 (2022) no. 10, p. 1376 | DOI:10.3390/e24101376
Huang, De; Niles-Weed, Jonathan; Tropp, Joel A.; Ward, Rachel Matrix Concentration for Products, Foundations of Computational Mathematics, Volume 22 (2022) no. 6, p. 1767 | DOI:10.1007/s10208-021-09533-9
Huang, Yi. C. On Poisson Semigroup Hypercontractivity for Higher-Dimensional Spheres, Functional Analysis and Its Applications, Volume 56 (2022) no. 3, p. 235 | DOI:10.1134/s001626632203008x
Ivanisvili, P.; Nazarov, F. On Weissler's conjecture on the Hamming cube. I, IMRN. International Mathematics Research Notices, Volume 2022 (2022) no. 9, pp. 6991-7020 | DOI:10.1093/imrn/rnaa363 | Zbl:1487.42069
Bafna, Mitali; Hopkins, Max; Kaufman, Tali; Lovett, Shachar, Proceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing (2022), p. 185 | DOI:10.1145/3519935.3520040
Huang, Yi C. О свойстве гиперсжатия полугруппы Пуассона для сфер высших размерностей, Функциональный анализ и его приложения, Volume 56 (2022) no. 3, p. 100 | DOI:10.4213/faa3975
Skorski, Maciej, 2021 55th Annual Conference on Information Sciences and Systems (CISS) (2021), p. 1 | DOI:10.1109/ciss50987.2021.9400306
Keller, Nathan; Lifshitz, Noam The junta method for hypergraphs and the Erdős-Chvátal simplex conjecture, Advances in Mathematics, Volume 392 (2021), p. 107991 | DOI:10.1016/j.aim.2021.107991
Kyrillidis, Anastasios; Shrivastava, Anshumali; Vardi, Moshe Y.; Zhang, Zhiwei Solving hybrid Boolean constraints in continuous space via multilinear Fourier expansions, Artificial Intelligence, Volume 299 (2021), p. 103559 | DOI:10.1016/j.artint.2021.103559
Mossel, Elchanan Probabilistic view of voting, paradoxes, and manipulation, Bulletin of the American Mathematical Society, Volume 59 (2021) no. 3, p. 297 | DOI:10.1090/bull/1751
Skorski, Maciej Hypercontractivity via Tensor Calculus, Computing and Combinatorics, Volume 13025 (2021), p. 449 | DOI:10.1007/978-3-030-89543-3_38
Skorski, Maciej Concentration of the Collision Estimator, Fundamentals of Computation Theory, Volume 12867 (2021), p. 440 | DOI:10.1007/978-3-030-86593-1_31
Kirshner, Naomi; Samorodnitsky, Alex A Moment Ratio Bound for Polynomials and Some Extremal Properties of Krawchouk Polynomials and Hamming Spheres, IEEE Transactions on Information Theory, Volume 67 (2021) no. 6, p. 3509 | DOI:10.1109/tit.2021.3071597
Sahasranand, K. R.; Tyagi, Himanshu Communication Complexity of Distributed High Dimensional Correlation Testing, IEEE Transactions on Information Theory, Volume 67 (2021) no. 9, p. 6082 | DOI:10.1109/tit.2021.3091773
Brannan, Michael; Vergnioux, Roland; Youn, Sang-Gyun Property RD and Hypercontractivity for Orthogonal Free Quantum Groups, International Mathematics Research Notices, Volume 2021 (2021) no. 2, p. 1573 | DOI:10.1093/imrn/rnaa118
Frank, Rupert L.; Ivanisvili, Paata Hypercontractivity of the semigroup of the fractional Laplacian on the n-sphere, Journal of Functional Analysis, Volume 281 (2021) no. 8, p. 109145 | DOI:10.1016/j.jfa.2021.109145
Beigi, Salman Improved quantum hypercontractivity inequality for the qubit depolarizing channel, Journal of Mathematical Physics, Volume 62 (2021) no. 12 | DOI:10.1063/5.0056388
Götze, Friedrich; Sambale, Holger; Sinulis, Arthur Concentration Inequalities for Bounded Functionals via Log-Sobolev-Type Inequalities, Journal of Theoretical Probability, Volume 34 (2021) no. 3, p. 1623 | DOI:10.1007/s10959-020-01016-x
Fawzi, Hamza On Polyhedral Approximations of the Positive Semidefinite Cone, Mathematics of Operations Research, Volume 46 (2021) no. 4, p. 1479 | DOI:10.1287/moor.2020.1077
Qin, Minglong; Yao, Penghui Nonlocal Games with Noisy Maximally Entangled States are Decidable, SIAM Journal on Computing, Volume 50 (2021) no. 6, p. 1800 | DOI:10.1137/20m134592x
Bakas, Odysseas On a Problem of Pichorides, The Journal of Geometric Analysis, Volume 31 (2021) no. 7, p. 7455 | DOI:10.1007/s12220-020-00550-8
Kelman, Esty; Kindler, Guy; Lifshitz, Noam; Minzer, Dor; Safra, Muli, 2020 IEEE 61st Annual Symposium on Foundations of Computer Science (FOCS) (2020), p. 247 | DOI:10.1109/focs46700.2020.00032
Ahle, Thomas D.; Knudsen, Jakob B. T., 2020 IEEE 61st Annual Symposium on Foundations of Computer Science (FOCS) (2020), p. 728 | DOI:10.1109/focs46700.2020.00073
Ivanisvili, Paata; Mooney, Connor Sharpening the triangle inequality : envelopes between L2 and Lp spaces, Analysis PDE, Volume 13 (2020) no. 5, p. 1591 | DOI:10.2140/apde.2020.13.1591
Aoki, Yosuke; Bennett, Jonathan; Bez, Neal; Machihara, Shuji; Matsuura, Kosuke; Shiraki, Shobu A supersolutions perspective on hypercontractivity, Annali di Matematica Pura ed Applicata (1923 -), Volume 199 (2020) no. 5, p. 2105 | DOI:10.1007/s10231-020-00958-7
Sambale, Holger; Sinulis, Arthur Logarithmic Sobolev inequalities for finite spin systems and applications, Bernoulli, Volume 26 (2020) no. 3 | DOI:10.3150/19-bej1172
Queffélec, Hervé; Queffélec, Martine Hardy Spaces of Dirichlet Series, Diophantine Approximation and Dirichlet Series, Volume 80 (2020), p. 145 | DOI:10.1007/978-981-15-9351-2_6
Kelman, Esty; Kindler, Guy; Lifshitz, Noam; Minzer, Dor; Safra, Muli Towards a Proof of the Fourier-Entropy Conjecture?, Geometric and Functional Analysis, Volume 30 (2020) no. 4, p. 1097 | DOI:10.1007/s00039-020-00544-2
Sudan, Madhu; Tyagi, Himanshu; Watanabe, Shun Communication for Generating Correlation: A Unifying Survey, IEEE Transactions on Information Theory, Volume 66 (2020) no. 1, p. 5 | DOI:10.1109/tit.2019.2946364
Ordentlich, Or; Polyanskiy, Yury; Shayevitz, Ofer A Note on the Probability of Rectangles for Correlated Binary Strings, IEEE Transactions on Information Theory, Volume 66 (2020) no. 12, p. 7878 | DOI:10.1109/tit.2020.3018232
Samorodnitsky, Alex An Upper Bound on $ℓ_{q}$ Norms of Noisy Functions, IEEE Transactions on Information Theory, Volume 66 (2020) no. 2, p. 742 | DOI:10.1109/tit.2019.2944698
Gavinsky, Dmitry Entangled Simultaneity Versus Classical Interactivity in Communication Complexity, IEEE Transactions on Information Theory, Volume 66 (2020) no. 7, p. 4641 | DOI:10.1109/tit.2020.2976074
Keller, Nathan; Klein, Ohad A structure theorem for almost low-degree functions on the slice, Israel Journal of Mathematics, Volume 240 (2020) no. 1, p. 179 | DOI:10.1007/s11856-020-2062-4
Kirshner, Naomi; Samorodnitsky, Alex On the ℓ4:ℓ2 ratio of functions with restricted Fourier support, Journal of Combinatorial Theory, Series A, Volume 172 (2020), p. 105202 | DOI:10.1016/j.jcta.2019.105202
Eskenazis, Alexandros; Ivanisvili, Paata Polynomial inequalities on the Hamming cube, Probability Theory and Related Fields, Volume 178 (2020) no. 1-2, p. 235 | DOI:10.1007/s00440-020-00973-y
Duminil-Copin, Hugo Lectures on the Ising and Potts Models on the Hypercubic Lattice, Random Graphs, Phase Transitions, and the Gaussian Free Field, Volume 304 (2020), p. 35 | DOI:10.1007/978-3-030-32011-9_2
Bafna, Mitali; Srinivasan, Srikanth; Sudan, Madhu Local decoding and testing of polynomials over grids, Random Structures Algorithms, Volume 57 (2020) no. 3, p. 658 | DOI:10.1002/rsa.20933
Bernstein, Megan; Damron, Michael; Greenwood, Torin Sublinear variance in Euclidean first-passage percolation, Stochastic Processes and their Applications, Volume 130 (2020) no. 8, p. 5060 | DOI:10.1016/j.spa.2020.02.011
Lifshitz, Noam; Minzer, Dor, 2019 IEEE 60th Annual Symposium on Foundations of Computer Science (FOCS) (2019), p. 1205 | DOI:10.1109/focs.2019.00075
Harper, Adam J Moments of random multiplicative functions, II: High moments, Algebra Number Theory, Volume 13 (2019) no. 10, p. 2277 | DOI:10.2140/ant.2019.13.2277
Bakas, Odysseas A variant of Yano’s extrapolation theorem on Hardy spaces, Archiv der Mathematik, Volume 113 (2019) no. 5, p. 537 | DOI:10.1007/s00013-019-01366-x
Defant, Andreas; García, Domingo; Maestre, Manuel; Sevilla-Peris, Pablo Dirichlet Series and Holomorphic Functions in High Dimensions, 2019 | DOI:10.1017/9781108691611
Adamczak, Radosław; Kotowski, Michał; Polaczyk, Bartłomiej; Strzelecki, Michał A note on concentration for polynomials in the Ising model, Electronic Journal of Probability, Volume 24 (2019) no. none | DOI:10.1214/19-ejp280
Duminil-Copin, Hugo Sharp threshold phenomena in statistical physics, Japanese Journal of Mathematics, Volume 14 (2019) no. 1, p. 1 | DOI:10.1007/s11537-018-1726-x
Bakas, Odysseas Variants of the Inequalities of Paley and Zygmund, Journal of Fourier Analysis and Applications, Volume 25 (2019) no. 3, p. 1113 | DOI:10.1007/s00041-018-9605-7
Polyanskiy, Yury; Samorodnitsky, Alex Improved log-Sobolev inequalities, hypercontractivity and uncertainty principle on the hypercube, Journal of Functional Analysis, Volume 277 (2019) no. 11, p. 108280 | DOI:10.1016/j.jfa.2019.108280
Cheng, Hao-Chung; Hsieh, Min-Hsiu Matrix Poincaré, Φ-Sobolev inequalities, and quantum ensembles, Journal of Mathematical Physics, Volume 60 (2019) no. 3 | DOI:10.1063/1.5035381
Filmus, Yuval; Mossel, Elchanan Harmonicity and invariance on slices of the Boolean cube, Probability Theory and Related Fields, Volume 175 (2019) no. 3-4, p. 721 | DOI:10.1007/s00440-019-00900-w
Bakas, Odysseas A multiplier inclusion theorem on product domains, Proceedings of the Edinburgh Mathematical Society, Volume 62 (2019) no. 4, p. 1073 | DOI:10.1017/s0013091519000087
Hastings, Matthew B. Duality in Quantum Quenches and Classical Approximation Algorithms: Pretty Good or Very Bad, Quantum, Volume 3 (2019), p. 201 | DOI:10.22331/q-2019-11-11-201
Weinberger, Nir; Shayevitz, Ofer Self-Predicting Boolean Functions, SIAM Journal on Discrete Mathematics, Volume 33 (2019) no. 2, p. 665 | DOI:10.1137/18m1207119
Polyanskiy, Yury Hypercontractivity of Spherical Averages in Hamming Space, SIAM Journal on Discrete Mathematics, Volume 33 (2019) no. 2, p. 731 | DOI:10.1137/15m1046575
Sahasranand, K. R.; Tyagi, Himanshu, 2018 IEEE International Symposium on Information Theory (ISIT) (2018), p. 2316 | DOI:10.1109/isit.2018.8437584
Weinberger, Nir; Shayevitz, Ofer, 2018 IEEE International Symposium on Information Theory (ISIT) (2018), p. 276 | DOI:10.1109/isit.2018.8437521
BOUYRIE, RAPHAËL On Quantitative Noise Stability and Influences for Discrete and Continuous Models, Combinatorics, Probability and Computing, Volume 27 (2018) no. 3, p. 334 | DOI:10.1017/s0963548318000044
Eldan, Ronen; Lee, James R. Regularization under diffusion and anticoncentration of the information content, Duke Mathematical Journal, Volume 167 (2018) no. 5 | DOI:10.1215/00127094-2017-0048
Berkowitz, Ross; Devlin, Pat A stability result using the matrix norm to bound the permanent, Israel Journal of Mathematics, Volume 224 (2018) no. 1, p. 437 | DOI:10.1007/s11856-018-1655-7
Keevash, Peter; Long, Eoin A stability result for the cube edge isoperimetric inequality, Journal of Combinatorial Theory, Series A, Volume 155 (2018), p. 360 | DOI:10.1016/j.jcta.2017.11.005
Feldman, Vitaly; Perkins, Will; Vempala, Santosh On the Complexity of Random Satisfiability Problems with Planted Solutions, SIAM Journal on Computing, Volume 47 (2018) no. 4, p. 1294 | DOI:10.1137/16m1078471
Kim, Hyeji; Gao, Weihao; Kannan, Sreeram; Oh, Sewoong; Viswanath, Pramod Discovering Potential Correlations via Hypercontractivity, Entropy, Volume 19 (2017) no. 11, p. 586 | DOI:10.3390/e19110586
Kane, Daniel A structure theorem for poorly anticoncentrated polynomials of Gaussians and applications to the study of polynomial threshold functions, The Annals of Probability, Volume 45 (2017) no. 3 | DOI:10.1214/16-aop1097
Heilman, Steven; Mossel, Elchanan; Oleszkiewicz, Krzysztof Strong contraction and influences in tail spaces, Transactions of the American Mathematical Society, Volume 369 (2017) no. 7, p. 4843 | DOI:10.1090/tran/6916
De, Anindya; Saks, Michael; Tang, Sijian, 2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS) (2016), p. 675 | DOI:10.1109/focs.2016.77
Ordentlich, Or; Shayevitz, Ofer; Weinstein, Omri, 2016 IEEE International Symposium on Information Theory (ISIT) (2016), p. 500 | DOI:10.1109/isit.2016.7541349
Traxler, Patrick The Relative Exponential Time Complexity of Approximate Counting Satisfying Assignments, Algorithmica, Volume 75 (2016) no. 2, p. 339 | DOI:10.1007/s00453-016-0134-y
Defant, Andreas; Mastyło, Mieczysław $L^{p}$ L p -Norms and Mahler’s Measure of Polynomials on the n-Dimensional Torus, Constructive Approximation, Volume 44 (2016) no. 1, p. 87 | DOI:10.1007/s00365-015-9319-x
Kamath, Sudeep; Anantharam, Venkat On Non-Interactive Simulation of Joint Distributions, IEEE Transactions on Information Theory, Volume 62 (2016) no. 6, p. 3419 | DOI:10.1109/tit.2016.2553672
Feldman, Vitaly; Vondrák, Jan Optimal Bounds on Approximation of Submodular and XOS Functions by Juntas, SIAM Journal on Computing, Volume 45 (2016) no. 3, p. 1129 | DOI:10.1137/140958207
Kamath, Sudeep, 2015 53rd Annual Allerton Conference on Communication, Control, and Computing (Allerton) (2015), p. 627 | DOI:10.1109/allerton.2015.7447063
Eldan, Ronen; Lee, James R., 2015 IEEE 56th Annual Symposium on Foundations of Computer Science (2015), p. 1395 | DOI:10.1109/focs.2015.89
Makarychev, Konstantin; Makarychev, Yury; Zhou, Yuan, 2015 IEEE 56th Annual Symposium on Foundations of Computer Science (2015), p. 975 | DOI:10.1109/focs.2015.64
Chen, Wei-Kuo; Dafnis, Nikos; Paouris, Grigoris Improved Hölder and reverse Hölder inequalities for Gaussian random vectors, Advances in Mathematics, Volume 280 (2015), p. 643 | DOI:10.1016/j.aim.2014.09.029
Miclo, Laurent On hyperboundedness and spectrum of Markov operators, Inventiones mathematicae, Volume 200 (2015) no. 1, p. 311 | DOI:10.1007/s00222-014-0538-8
Cubitt, Toby; Kastoryano, Michael; Montanaro, Ashley; Temme, Kristan Quantum reverse hypercontractivity, Journal of Mathematical Physics, Volume 56 (2015) no. 10 | DOI:10.1063/1.4933219
Junge, Marius; Palazuelos, Carlos; Parcet, Javier; Perrin, Mathilde Hypercontractivity in finite-dimensional matrix algebras, Journal of Mathematical Physics, Volume 56 (2015) no. 2 | DOI:10.1063/1.4907378
Adamczak, Radosław; Wolff, Paweł Concentration inequalities for non-Lipschitz functions with bounded derivatives of higher order, Probability Theory and Related Fields, Volume 162 (2015) no. 3-4, p. 531 | DOI:10.1007/s00440-014-0579-3
Damron, Michael; Hanson, Jack; Sosoe, Philippe Sublinear variance in first-passage percolation for general distributions, Probability Theory and Related Fields, Volume 163 (2015) no. 1-2, p. 223 | DOI:10.1007/s00440-014-0591-7
Tamaki, Suguru; Yoshida, Yuichi A query efficient non-adaptive long code test with perfect completeness, Random Structures Algorithms, Volume 47 (2015) no. 2, p. 386 | DOI:10.1002/rsa.20549
Keller, Nathan; Mossel, Elchanan; Sen, Arnab Geometric influences II: Correlation inequalities and noise sensitivity, Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, Volume 50 (2014) no. 4 | DOI:10.1214/13-aihp557
King, Christopher Hypercontractivity for Semigroups of Unital Qubit Channels, Communications in Mathematical Physics, Volume 328 (2014) no. 1, p. 285 | DOI:10.1007/s00220-014-1982-4
Defant, Andreas; Sevilla-Peris, Pablo The Bohnenblust-Hille cycle of ideas from a modern point of view, Functiones et Approximatio Commentarii Mathematici, Volume 50 (2014) no. 1 | DOI:10.7169/facm/2014.50.1.2
Ledoux, Michel Remarks on Gaussian Noise Stability, Brascamp-Lieb and Slepian Inequalities, Geometric Aspects of Functional Analysis, Volume 2116 (2014), p. 309 | DOI:10.1007/978-3-319-09477-9_20
Oleszkiewicz, Krzysztof Precise moment and tail bounds for Rademacher sums in terms of weak parameters, Israel Journal of Mathematics, Volume 203 (2014) no. 1, p. 429 | DOI:10.1007/s11856-014-1109-9
Lee, James R.; Gharan, Shayan Oveis; Trevisan, Luca Multiway Spectral Partitioning and Higher-Order Cheeger Inequalities, Journal of the ACM, Volume 61 (2014) no. 6, p. 1 | DOI:10.1145/2665063
Traxler, Patrick The Relative Exponential Time Complexity of Approximate Counting Satisfying Assignments, Parameterized and Exact Computation, Volume 8894 (2014), p. 332 | DOI:10.1007/978-3-319-13524-3_28
De, Anindya; Servedio, Rocco A., Proceedings of the forty-sixth annual ACM symposium on Theory of computing (2014), p. 832 | DOI:10.1145/2591796.2591800
Mendel, Manor; Naor, Assaf Nonlinear spectral calculus and super-expanders, Publications mathématiques de l'IHÉS, Volume 119 (2014) no. 1, p. 1 | DOI:10.1007/s10240-013-0053-2
Diakonikolas, Ilias; Raghavendra, Prasad; Servedio, Rocco A.; Tan, Li-Yang Average Sensitivity and Noise Sensitivity of Polynomial Threshold Functions, SIAM Journal on Computing, Volume 43 (2014) no. 1, p. 231 | DOI:10.1137/110855223
Chatterjee, Sourav Independent Flips, Superconcentration and Related Topics (2014), p. 63 | DOI:10.1007/978-3-319-03886-5_7
Kane, Daniel M. The correct exponent for the Gotsman–Linial Conjecture, computational complexity, Volume 23 (2014) no. 2, p. 151 | DOI:10.1007/s00037-014-0086-z
Anantharam, Venkat; Gohari, Amin Aminzadeh; Kamath, Sudeep; Nair, Chandra, 2013 51st Annual Allerton Conference on Communication, Control, and Computing (Allerton) (2013), p. 13 | DOI:10.1109/allerton.2013.6736499
Kane, Daniel M., 2013 IEEE Conference on Computational Complexity (2013), p. 56 | DOI:10.1109/ccc.2013.15
O'Donnell, Ryan; Wimmer, Karl Sharpness of KKL on Schreier graphs, Electronic Communications in Probability, Volume 18 (2013) no. none | DOI:10.1214/ecp.v18-1961
Downey, Rodney G.; Fellows, Michael R. Color Coding, Multilinear Detection, and Randomized Divide and Conquer, Fundamentals of Parameterized Complexity (2013), p. 143 | DOI:10.1007/978-1-4471-5559-1_8
Mossel, Elchanan; Oleszkiewicz, Krzysztof; Sen, Arnab On Reverse Hypercontractivity, Geometric and Functional Analysis, Volume 23 (2013) no. 3, p. 1062 | DOI:10.1007/s00039-013-0229-4
Graham, Colin C.; Hare, Kathryn E. Hadamard Sets, Interpolation and Sidon Sets for Compact Groups (2013), p. 1 | DOI:10.1007/978-1-4614-5392-5_1
Graham, Colin C.; Hare, Kathryn E. Sidon Sets Are Proportional Quasi-independent, Interpolation and Sidon Sets for Compact Groups (2013), p. 117 | DOI:10.1007/978-1-4614-5392-5_7
Graham, Colin C.; Hare, Kathryn E. How Thin Are Sidon Sets in the Bohr Compactification?, Interpolation and Sidon Sets for Compact Groups (2013), p. 135 | DOI:10.1007/978-1-4614-5392-5_8
Graham, Colin C.; Hare, Kathryn E. The Relationship Between Sidon and I 0, Interpolation and Sidon Sets for Compact Groups (2013), p. 153 | DOI:10.1007/978-1-4614-5392-5_9
Graham, Colin C.; Hare, Kathryn E. Sets of Zero Discrete Harmonic Density, Interpolation and Sidon Sets for Compact Groups (2013), p. 175 | DOI:10.1007/978-1-4614-5392-5_10
Graham, Colin C.; Hare, Kathryn E. ε-Kronecker Sets, Interpolation and Sidon Sets for Compact Groups (2013), p. 19 | DOI:10.1007/978-1-4614-5392-5_2
Graham, Colin C.; Hare, Kathryn E. I 0 Sets and Their Characterizations, Interpolation and Sidon Sets for Compact Groups (2013), p. 49 | DOI:10.1007/978-1-4614-5392-5_3
Graham, Colin C.; Hare, Kathryn E. More Restrictive Classes of I 0 Sets, Interpolation and Sidon Sets for Compact Groups (2013), p. 67 | DOI:10.1007/978-1-4614-5392-5_4
Graham, Colin C.; Hare, Kathryn E. Unions and Decompositions of I 0(U) Sets, Interpolation and Sidon Sets for Compact Groups (2013), p. 77 | DOI:10.1007/978-1-4614-5392-5_5
Graham, Colin C.; Hare, Kathryn E. Sidon Sets: Introduction and Decomposition Properties, Interpolation and Sidon Sets for Compact Groups (2013), p. 93 | DOI:10.1007/978-1-4614-5392-5_6
Ball, K.; Barthe, F.; Bednorz, W.; Oleszkiewicz, K.; Wolff, P. L 1 ‐SMOOTHING FOR THE ORNSTEIN–UHLENBECK SEMIGROUP, Mathematika, Volume 59 (2013) no. 1, p. 160 | DOI:10.1112/s0025579312001064
Major, Péter An Overview of the Results and a Discussion of the Literature, On the Estimation of Multiple Random Integrals and U-Statistics, Volume 2079 (2013), p. 227 | DOI:10.1007/978-3-642-37617-7_18
Haviv, Ishay; Langberg, Michael, Proceedings of the 4th conference on Innovations in Theoretical Computer Science (2013), p. 541 | DOI:10.1145/2422436.2422495
De, Anindya; Mossel, Elchanan; Neeman, Joe, Proceedings of the forty-fifth annual ACM symposium on Theory of Computing (2013), p. 477 | DOI:10.1145/2488608.2488668
Diakonikolas, Ilias; Servedio, Rocco A. Improved Approximation of Linear Threshold Functions, computational complexity, Volume 22 (2013) no. 3, p. 623 | DOI:10.1007/s00037-012-0045-5
Kane, Daniel M., 2012 IEEE 53rd Annual Symposium on Foundations of Computer Science (2012), p. 91 | DOI:10.1109/focs.2012.52
Adamczak, Radosław; Latała, Rafał Tail and moment estimates for chaoses generated by symmetric random variables with logarithmically concave tails, Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, Volume 48 (2012) no. 4 | DOI:10.1214/11-aihp441
Keller, Nathan; Mossel, Elchanan; Schlank, Tomer A note on the Entropy/Influence conjecture, Discrete Mathematics, Volume 312 (2012) no. 22, p. 3364 | DOI:10.1016/j.disc.2012.07.031
Keller, Nathan A simple reduction from a biased measure on the discrete cube to the uniform measure, European Journal of Combinatorics, Volume 33 (2012) no. 8, p. 1943 | DOI:10.1016/j.ejc.2012.06.003
Cordero-Erausquin, Dario; Ledoux, Michel Hypercontractive Measures, Talagrand’s Inequality, and Influences, Geometric Aspects of Functional Analysis, Volume 2050 (2012), p. 169 | DOI:10.1007/978-3-642-29849-3_10
Gutin, Gregory; van Iersel, Leo; Mnich, Matthias; Yeo, Anders Every ternary permutation constraint satisfaction problem parameterized above average has a kernel with a quadratic number of variables, Journal of Computer and System Sciences, Volume 78 (2012) no. 1, p. 151 | DOI:10.1016/j.jcss.2011.01.004
Montanaro, Ashley Some applications of hypercontractive inequalities in quantum information theory, Journal of Mathematical Physics, Volume 53 (2012) no. 12 | DOI:10.1063/1.4769269
Lau, Yuk-Kam; Tenenbaum, Gérald; Wu, Jie On mean values of random multiplicative functions, Proceedings of the American Mathematical Society, Volume 141 (2012) no. 2, p. 409 | DOI:10.1090/s0002-9939-2012-11332-2
Gutin, Gregory; Yeo, Anders Constraint Satisfaction Problems Parameterized above or below Tight Bounds: A Survey, The Multivariate Algorithmic Revolution and Beyond, Volume 7370 (2012), p. 257 | DOI:10.1007/978-3-642-30891-8_14
Alon, Noga; Gutin, Gregory; Kim, Eun Jung; Szeider, Stefan; Yeo, Anders Solving MAX-r-SAT Above a Tight Lower Bound, Algorithmica, Volume 61 (2011) no. 3, p. 638 | DOI:10.1007/s00453-010-9428-7
Defant, Andreas; Frerick, Leonhard; Ortega-Cerdà, Joaquim; Ounaïes, Myriam; Seip, Kristian The Bohnenblust-Hille inequality for homogeneous polynomials is hypercontractive, Annals of Mathematics, Volume 174 (2011) no. 1, p. 485 | DOI:10.4007/annals.2011.174.1.13
KELLER, NATHAN On the Influences of Variables on Boolean Functions in Product Spaces, Combinatorics, Probability and Computing, Volume 20 (2011) no. 1, p. 83 | DOI:10.1017/s0963548310000234
Bogdanov, Andrej; Mossel, Elchanan On Extracting Common Random Bits From Correlated Sources, IEEE Transactions on Information Theory, Volume 57 (2011) no. 10, p. 6351 | DOI:10.1109/tit.2011.2134067
Defant, Andreas; Frerick, Leonhard The Bohr radius of the unit ball of, Journal für die reine und angewandte Mathematik (Crelles Journal), Volume 2011 (2011) no. 660 | DOI:10.1515/crelle.2011.080
Gutin, Gregory; Kim, Eun Jung; Szeider, Stefan; Yeo, Anders A probabilistic approach to problems parameterized above or below tight bounds, Journal of Computer and System Sciences, Volume 77 (2011) no. 2, p. 422 | DOI:10.1016/j.jcss.2010.06.001
Blei, Ron Measurements of interdependence, Lithuanian Mathematical Journal, Volume 51 (2011) no. 2, p. 141 | DOI:10.1007/s10986-011-9114-8
Regev, Oded; Klartag, Bo'az, Proceedings of the forty-third annual ACM symposium on Theory of computing (2011), p. 31 | DOI:10.1145/1993636.1993642
Austrin, Per; HÅstad, Johan Randomly Supported Independence and Resistance, SIAM Journal on Computing, Volume 40 (2011) no. 1, p. 1 | DOI:10.1137/100783534
Montanari, Andrea; Restrepo, Ricardo; Tetali, Prasad Reconstruction and Clustering in Random Constraint Satisfaction Problems, SIAM Journal on Discrete Mathematics, Volume 25 (2011) no. 2, p. 771 | DOI:10.1137/090755862
Benjamini, Itai; Kalai, Gn.; Schramm, Oded Noise Sensitivity of Boolean Functions and Applications to Percolation, Selected Works of Oded Schramm (2011), p. 351 | DOI:10.1007/978-1-4419-9675-6_12
Benjamini, Itai; Kalai, Gil; Schramm, Oded First Passage Percolation Has Sublinear Distance Variance, Selected Works of Oded Schramm (2011), p. 779 | DOI:10.1007/978-1-4419-9675-6_26
Diakonikolas, Ilias; Servedio, Rocco A.; Tan, Li-Yang; Wan, Andrew, 2010 IEEE 25th Annual Conference on Computational Complexity (2010), p. 211 | DOI:10.1109/ccc.2010.28
Diakonikolas, Ilias; Kane, Daniel M.; Nelson, Jelani, 2010 IEEE 51st Annual Symposium on Foundations of Computer Science (2010), p. 11 | DOI:10.1109/focs.2010.8
Charikar, Moses; Leighton, Tom; Li, Shi; Moitra, Ankur, 2010 IEEE 51st Annual Symposium on Foundations of Computer Science (2010), p. 265 | DOI:10.1109/focs.2010.32
Gutin, Gregory; van Iersel, Leo; Mnich, Matthias; Yeo, Anders All Ternary Permutation Constraint Satisfaction Problems Parameterized above Average Have Kernels with Quadratic Numbers of Variables, Algorithms – ESA 2010, Volume 6346 (2010), p. 326 | DOI:10.1007/978-3-642-15775-2_28
Tamaki, Suguru; Yoshida, Yuichi A Query Efficient Non-adaptive Long Code Test with Perfect Completeness, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, Volume 6302 (2010), p. 738 | DOI:10.1007/978-3-642-15369-3_55
Mossel, Elchanan Gaussian Bounds for Noise Correlation of Functions, Geometric and Functional Analysis, Volume 19 (2010) no. 6, p. 1713 | DOI:10.1007/s00039-010-0047-x
Keller, Nathan On the probability of a rational outcome for generalized social welfare functions on three alternatives, Journal of Combinatorial Theory, Series A, Volume 117 (2010) no. 4, p. 389 | DOI:10.1016/j.jcta.2009.10.008
Gutin, Gregory; Kim, Eun Jung; Mnich, Matthias; Yeo, Anders Betweenness parameterized above tight lower bound, Journal of Computer and System Sciences, Volume 76 (2010) no. 8, p. 872 | DOI:10.1016/j.jcss.2010.05.001
Graczyk, Piotr; Kemp, Todd; Loeb, Jean-Jacques Hypercontractivity for log-subharmonic functions, Journal of Functional Analysis, Volume 258 (2010) no. 6, p. 1785 | DOI:10.1016/j.jfa.2009.08.014
Diakonikolas, Ilias; Servedio, Rocco A., 2009 24th Annual IEEE Conference on Computational Complexity (2009), p. 161 | DOI:10.1109/ccc.2009.8
HATAMI, HAMED Decision Trees and Influences of Variables Over Product Probability Spaces, Combinatorics, Probability and Computing, Volume 18 (2009) no. 3, p. 357 | DOI:10.1017/s0963548309009833
Blei, Ron; Ge, Lin Relationships between combinatorial measurements and Orlicz norms (II), Journal of Functional Analysis, Volume 257 (2009) no. 12, p. 3949 | DOI:10.1016/j.jfa.2009.04.010
Blei, Ron; Ge, Lin Relationships between combinatorial measurements and Orlicz norms, Journal of Functional Analysis, Volume 257 (2009) no. 3, p. 683 | DOI:10.1016/j.jfa.2009.02.020
Austrin, Per; Håstad, Johan, Proceedings of the forty-first annual ACM symposium on Theory of computing (2009), p. 483 | DOI:10.1145/1536414.1536481
Gavinsky, Dmitry; Kempe, Julia; Kerenidis, Iordanis; Raz, Ran; de Wolf, Ronald Exponential Separation for One-Way Quantum Communication Complexity, with Applications to Cryptography, SIAM Journal on Computing, Volume 38 (2009) no. 5, p. 1695 | DOI:10.1137/070706550
Chen, Guan-Yu; Liu, Wai-Wai; Saloff-Coste, Laurent The logarithmic Sobolev constant of some finite Markov chains, Annales de la Faculté des sciences de Toulouse : Mathématiques, Volume 17 (2008) no. 2, p. 239 | DOI:10.5802/afst.1183
Sereni, Jean-Sébastien Randomly colouring graphs (a combinatorial view), Computer Science Review, Volume 2 (2008) no. 2, p. 63 | DOI:10.1016/j.cosrev.2008.05.003
Villani, C. Entropy Production and Convergence to Equilibrium, Entropy Methods for the Boltzmann Equation, Volume 1916 (2008), p. 1 | DOI:10.1007/978-3-540-73705-6_1
O'Donnell, Ryan, Proceedings of the fortieth annual ACM symposium on Theory of computing (2008), p. 569 | DOI:10.1145/1374376.1374458
Motwani, Rajeev; Naor, Assaf; Panigrahy, Rina Lower Bounds on Locality Sensitive Hashing, SIAM Journal on Discrete Mathematics, Volume 21 (2008) no. 4, p. 930 | DOI:10.1137/050646858
Devroye, Luc; Lugosi, Gábor Local tail bounds for functions of independent random variables, The Annals of Probability, Volume 36 (2008) no. 1 | DOI:10.1214/00911797000000088
FALIK, DVIR; SAMORODNITSKY, ALEX Edge-Isoperimetric Inequalities and Influences, Combinatorics, Probability and Computing, Volume 16 (2007) no. 05, p. 693 | DOI:10.1017/s0963548306008340
Dinur, Irit; Friedgut, Ehud; Kindler, Guy; O’Donnell, Ryan On the Fourier tails of bounded functions over the discrete cube, Israel Journal of Mathematics, Volume 160 (2007) no. 1, p. 389 | DOI:10.1007/s11856-007-0068-9
Alon, Noga; Andoni, Alexandr; Kaufman, Tali; Matulef, Kevin; Rubinfeld, Ronitt; Xie, Ning, Proceedings of the thirty-ninth annual ACM symposium on Theory of computing (2007), p. 496 | DOI:10.1145/1250790.1250863
Gavinsky, Dmitry; Kempe, Julia; Kerenidis, Iordanis; Raz, Ran; de Wolf, Ronald, Proceedings of the thirty-ninth annual ACM symposium on Theory of computing (2007), p. 516 | DOI:10.1145/1250790.1250866
Arpe, Jan; Reischuk, Rüdiger Learning juntas in the presence of noise, Theoretical Computer Science, Volume 384 (2007) no. 1, p. 2 | DOI:10.1016/j.tcs.2007.05.014
Major, Peter A multivariate version of Hoeffding's inequality, Electronic Communications in Probability, Volume 11 (2006) no. none | DOI:10.1214/ecp.v11-1221
Haupt, J.; Nowak, R. Signal Reconstruction From Noisy Random Projections, IEEE Transactions on Information Theory, Volume 52 (2006) no. 9, p. 4036 | DOI:10.1109/tit.2006.880031
Alon, Noga; Makarychev, Konstantin; Makarychev, Yury; Naor, Assaf Quadratic forms on graphs, Inventiones mathematicae, Volume 163 (2006) no. 3, p. 499 | DOI:10.1007/s00222-005-0465-9
Mossel, Elchanan; O'Donnell, Ryan; Regev, Oded; Steif, Jeffrey E.; Sudakov, Benny Non-interactive correlation distillation, inhomogeneous Markov chains, and the reverse Bonami-Beckner inequality, Israel Journal of Mathematics, Volume 154 (2006) no. 1, p. 299 | DOI:10.1007/bf02773611
Tao, Terence; Vu, Van On random ±1 matrices: Singularity and determinant, Random Structures Algorithms, Volume 28 (2006) no. 1, p. 1 | DOI:10.1002/rsa.20109
Rossignol, Raphaël Threshold for monotone symmetric properties through a logarithmic Sobolev inequality, The Annals of Probability, Volume 34 (2006) no. 5 | DOI:10.1214/009117906000000287
Arpe, Jan; Reischuk, Rüdiger Learning Juntas in the Presence of Noise, Theory and Applications of Models of Computation, Volume 3959 (2006), p. 387 | DOI:10.1007/11750321_37
Mossel, E.; O'Donnell, R.; Oleszkiewicz, K., 46th Annual IEEE Symposium on Foundations of Computer Science (FOCS'05) (2005), p. 21 | DOI:10.1109/sfcs.2005.53
Alon, Noga; Makarychev, Konstantin; Makarychev, Yury; Naor, Assaf, Proceedings of the thirty-seventh annual ACM symposium on Theory of computing (2005), p. 486 | DOI:10.1145/1060590.1060664
Mossel, Elchanan; O'Donnell, Ryan Coin flipping from a cosmic source: On error correction of truly random bits, Random Structures Algorithms, Volume 26 (2005) no. 4, p. 418 | DOI:10.1002/rsa.20062
Boucheron, Stéphane; Bousquet, Olivier; Lugosi, Gábor; Massart, Pascal Moment inequalities for functions of independent random variables, The Annals of Probability, Volume 33 (2005) no. 2 | DOI:10.1214/009117904000000856
Blei, Ron; Janson, Svante Rademacher chaos: tail estimates versus limit theorems, Arkiv för Matematik, Volume 42 (2004) no. 1, p. 13 | DOI:10.1007/bf02432908
Håstad, Johan; Venkatesh, S. On the advantage over a random assignment, Random Structures Algorithms, Volume 25 (2004) no. 2, p. 117 | DOI:10.1002/rsa.20031
Friedgut, Ehud Hypergraphs, Entropy, and Inequalities, The American Mathematical Monthly, Volume 111 (2004) no. 9, p. 749 | DOI:10.1080/00029890.2004.11920139
Pisier, Gilles; Xu, Quanhua Non-Commutative Lp-Spaces, Volume 2 (2003), p. 1459 | DOI:10.1016/s1874-5849(03)80041-4
Benjamini, Itai; Kalai, Gil; Schramm, Oded First passage percolation has sublinear distance variance, The Annals of Probability, Volume 31 (2003) no. 4 | DOI:10.1214/aop/1068646373
Friedgut, Ehud; Kalai, Gil; Naor, Assaf Boolean functions whose Fourier transform is concentrated on the first two levels, Advances in Applied Mathematics, Volume 29 (2002) no. 3, p. 427 | DOI:10.1016/s0196-8858(02)00024-6
Friedgut, Ehud; Rödl, Vojtech Proof of a hypercontractive estimate via entropy, Israel Journal of Mathematics, Volume 125 (2001) no. 1, p. 369 | DOI:10.1007/bf02773387
Latała, Rafał; Zinn, Joel Necessary and sufficient conditions for the strong law of large numbers for U-statistics, The Annals of Probability, Volume 28 (2000) no. 4 | DOI:10.1214/aop/1019160513
Kalai, Gil Combinatorics with a Geometric Flavor, Visions in Mathematics (2000), p. 742 | DOI:10.1007/978-3-0346-0425-3_7
Benjamini, Itai; Kalai, Gil; Schramm, Oded Noise sensitivity of Boolean functions and applications to percolation, Publications mathématiques de l'IHÉS, Volume 90 (1999) no. 1, p. 5 | DOI:10.1007/bf02698830
Ledoux, Michel Concentration of measure and logarithmic Sobolev inequalities, Séminaire de Probabilités XXXIII, Volume 1709 (1999), p. 120 | DOI:10.1007/bfb0096511
Hitczenko, Pawel; Kwapien, Stanislaw; Li, Wenbo; Schechtman, Gideon; Schlumprecht, Thomas; Zinn, Joel Hypercontractivity and Comparison of Moments of Iterated Maxima and Minima of Independent Random Variables, Electronic Journal of Probability, Volume 3 (1998) no. none | DOI:10.1214/ejp.v3-24
Friedgut, Ehud; Kahn, Jeff On the number of copies of one hypergraph in another, Israel Journal of Mathematics, Volume 105 (1998) no. 1, p. 251 | DOI:10.1007/bf02780332
Bobkov, S.G; Ledoux, M On Modified Logarithmic Sobolev Inequalities for Bernoulli and Poisson Measures, Journal of Functional Analysis, Volume 156 (1998) no. 2, p. 347 | DOI:10.1006/jfan.1997.3187
Hazewinkel, M. H, Encyclopaedia of Mathematics (1997), p. 280 | DOI:10.1007/978-94-015-1288-6_8
Gine, Evarist Decoupling and limit theorems for u-statistics and u-processes, Lectures on Probability Theory and Statistics, Volume 1665 (1997), p. 1 | DOI:10.1007/bfb0092618
Saloff-Coste, Laurent Lectures on finite Markov chains, Lectures on Probability Theory and Statistics, Volume 1665 (1997), p. 301 | DOI:10.1007/bfb0092621
Ledoux, Michel Isoperimetry and Gaussian analysis, Lectures on Probability Theory and Statistics, Volume 1648 (1996), p. 165 | DOI:10.1007/bfb0095676
Igari, Satoru; Sato, Enji Operating functions on Fourier multipliers, Tohoku Mathematical Journal, Volume 46 (1994) no. 3 | DOI:10.2748/tmj/1178225717
Gross, Leonard Logarithmic Sobolev inequalities and contractivity properties of semigroups, Dirichlet Forms, Volume 1563 (1993), p. 54 | DOI:10.1007/bfb0074091
Arcones, Miguel A.; Gin�, Evarist On decoupling, series expansions, and tail behavior of chaos processes, Journal of Theoretical Probability, Volume 6 (1993) no. 1, p. 101 | DOI:10.1007/bf01046771
Hare, Kathryn E.; Wilson, David C. A structural criterion for the existence of infinite central Λ(𝑝) sets, Transactions of the American Mathematical Society, Volume 337 (1993) no. 2, p. 907 | DOI:10.1090/s0002-9947-1993-1157613-2
Giné, Evarist; Zinn, Joel On Hoffmann-JØrgensen’s Inequality for U-Processes, Probability in Banach Spaces, 8: (1992), p. 80 | DOI:10.1007/978-1-4612-0367-4_5
Rieders, Eric Marcinkiewicz-type strong laws for partially exchangeable arrays, Journal of Multivariate Analysis, Volume 38 (1991) no. 1, p. 114 | DOI:10.1016/0047-259x(91)90035-z
Ledoux, Michel; Talagrand, Michel Rademacher Averages, Probability in Banach Spaces (1991), p. 89 | DOI:10.1007/978-3-642-20212-4_6
Graham, Colin C; Hare, Kathryn E; Ritter, David L The size of Lp-improving measures, Journal of Functional Analysis, Volume 84 (1989) no. 2, p. 472 | DOI:10.1016/0022-1236(89)90106-7
Hare, Kathryn E. Lp-improving measures on compact non-abelian groups, Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics, Volume 46 (1989) no. 3, p. 402 | DOI:10.1017/s1446788700030895
Vrem, R. C. Lp-improving measures on hypergroups, Probability Measures on Groups IX, Volume 1379 (1989), p. 389 | DOI:10.1007/bfb0087865
Krakowiak, Wieslaw; Szulga, Jerzy Hypercontraction principle and random multilinear forms, Probability Theory and Related Fields, Volume 77 (1988) no. 3, p. 325 | DOI:10.1007/bf00319292
Hare, Kathryn E. A characterization of 𝐿^𝑝-improving measures, Proceedings of the American Mathematical Society, Volume 102 (1988) no. 2, p. 295 | DOI:10.1090/s0002-9939-1988-0920989-6
Ledoux, M.; Marcus, M. B. Some remarks on the uniform convergence of Gaussian and Rademacher Fourier quadratic forms, Geometrical and Statistical Aspects of Probability in Banach Spaces, Volume 1193 (1986), p. 53 | DOI:10.1007/bfb0077100
Ritter, David L. Most Riesz product measures are 𝐿^𝑝-improving, Proceedings of the American Mathematical Society, Volume 97 (1986) no. 2, p. 291 | DOI:10.1090/s0002-9939-1986-0835883-7
Bourgain, J.; Davis, W. J. Martingale transforms and complex uniform convexity, Transactions of the American Mathematical Society, Volume 294 (1986) no. 2, p. 501 | DOI:10.1090/s0002-9947-1986-0825718-5
Fournier, John J. F.; Ross, Kenneth A. Random Fourier series on compact abelian hypergroups, Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics, Volume 37 (1984) no. 1, p. 45 | DOI:10.1017/s1446788700021741
Ritter, David L. Convolution inequalities on finite cyclic groups and the pseudomeasure norm, Proceedings of the American Mathematical Society, Volume 91 (1984) no. 4, p. 589 | DOI:10.1090/s0002-9939-1984-0746095-8
Janson, Svante On hypercontractivity for multipliers on orthogonal polynomials, Arkiv för Matematik, Volume 21 (1983) no. 1-2, p. 97 | DOI:10.1007/bf02384302
Bourgain, J. Embedding 𝐿¹ in 𝐿¹/𝐻¹, Transactions of the American Mathematical Society, Volume 278 (1983) no. 2, p. 689 | DOI:10.1090/s0002-9947-1983-0701518-9
Borell, Christer Positivity improving operators and hypercontractivity, Mathematische Zeitschrift, Volume 180 (1982) no. 3, p. 225 | DOI:10.1007/bf01318906
Fournier, John J. F. Two UC-sets whose union is not a UC-set, Proceedings of the American Mathematical Society, Volume 84 (1982) no. 1, p. 69 | DOI:10.1090/s0002-9939-1982-0633280-7
Baronti, Marco; Foresti, Genzianella An example of asymmetry of convolution operators, Rendiconti del Circolo Matematico di Palermo, Volume 31 (1982) no. 3, p. 341 | DOI:10.1007/bf02851145
Bloom, Walter R. Approximation Theory on the Compact Solenoid, Functional Analysis and Approximation (1981), p. 167 | DOI:10.1007/978-3-0348-9369-5_17
Blei, Ron C. Fractional cartesian products in harmonic analysis, Harmonic Analysis Iraklion 1978, Volume 781 (1980), p. 8 | DOI:10.1007/bfb0097642
Weissler, Fred B Logarithmic Sobolev inequalities and hypercontractive estimates on the circle, Journal of Functional Analysis, Volume 37 (1980) no. 2, p. 218 | DOI:10.1016/0022-1236(80)90042-7
Gaudry, Garth I. Spectral Littlewood-Paley decompositions, Tohoku Mathematical Journal, Volume 32 (1980) no. 3 | DOI:10.2748/tmj/1178229595
Oberlin, Daniel M. Singular measures andl p Fourier transforms, Israel Journal of Mathematics, Volume 34 (1979) no. 1-2, p. 115 | DOI:10.1007/bf02761828
Pigno, Louis Fourier-Stieltjes Transforms which vanish at infinity off certain sets, Glasgow Mathematical Journal, Volume 19 (1978) no. 1, p. 49 | DOI:10.1017/s0017089500003360
Gaudry, Garth I. Littlewood–Paley theorems for sum and difference sets, Mathematical Proceedings of the Cambridge Philosophical Society, Volume 83 (1978) no. 1, p. 65 | DOI:10.1017/s0305004100054293
Pisier, Gilles; Zinn, Joel On the limit theorems for random variables with values in the spaces L p (2?p, Zeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete, Volume 41 (1978) no. 4, p. 289 | DOI:10.1007/bf00533600
Oberlin, Daniel M. 𝑝-Helson sets, Proceedings of the American Mathematical Society, Volume 54 (1976) no. 1, p. 173 | DOI:10.1090/s0002-9939-1976-0420152-3
Oberlin, Daniel M. Multipliers of 𝐿^𝑝_𝐸. I, Transactions of the American Mathematical Society, Volume 221 (1976) no. 1, p. 187 | DOI:10.1090/s0002-9947-1976-0402417-9
Oberlin, Daniel M. Multipliers of closed ideals of 𝐿^𝑝(𝐷^∞), Bulletin of the American Mathematical Society, Volume 81 (1975) no. 2, p. 479 | DOI:10.1090/s0002-9904-1975-13791-8
Oberlin, Daniel M. M p(G)≠M q(G) (p −1+q −=1), Israel Journal of Mathematics, Volume 22 (1975) no. 2, p. 175 | DOI:10.1007/bf02760165
Blei, Ron C. A tensor approach to interpolation phenomena in discrete abelian groups, Proceedings of the American Mathematical Society, Volume 49 (1975) no. 1, p. 175 | DOI:10.1090/s0002-9939-1975-0361626-2
Edwards, R.E; Ross, Kenneth A p-Sidon sets, Journal of Functional Analysis, Volume 15 (1974) no. 4, p. 404 | DOI:10.1016/0022-1236(74)90031-7
Figà-Talamanca, Alessandro Multipliers vanishing at infinity for certain compact groups, Proceedings of the American Mathematical Society, Volume 45 (1974) no. 2, p. 199 | DOI:10.1090/s0002-9939-1974-0461035-0

Cité par 245 documents. Sources : Crossref, zbMATH