The dual of weak Lp
Annales de l'Institut Fourier, Tome 25 (1975) no. 2, pp. 81-126.

Soit 1<p<. Nous donnons une caractérisation de l’espace dual de Lp-faible sur un espace mesuré non-atomique.

For 1<p<, a characterization is given of the dual space of weak Lp taken over a non atomic measure space.

@article{AIF_1975__25_2_81_0,
     author = {Cwikel, Michael},
     title = {The dual of weak $L^p$},
     journal = {Annales de l'Institut Fourier},
     pages = {81--126},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {25},
     number = {2},
     year = {1975},
     doi = {10.5802/aif.556},
     mrnumber = {53 #11355},
     zbl = {0301.46025},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/aif.556/}
}
TY  - JOUR
AU  - Cwikel, Michael
TI  - The dual of weak $L^p$
JO  - Annales de l'Institut Fourier
PY  - 1975
SP  - 81
EP  - 126
VL  - 25
IS  - 2
PB  - Institut Fourier
PP  - Grenoble
UR  - http://www.numdam.org/articles/10.5802/aif.556/
DO  - 10.5802/aif.556
LA  - en
ID  - AIF_1975__25_2_81_0
ER  - 
%0 Journal Article
%A Cwikel, Michael
%T The dual of weak $L^p$
%J Annales de l'Institut Fourier
%D 1975
%P 81-126
%V 25
%N 2
%I Institut Fourier
%C Grenoble
%U http://www.numdam.org/articles/10.5802/aif.556/
%R 10.5802/aif.556
%G en
%F AIF_1975__25_2_81_0
Cwikel, Michael. The dual of weak $L^p$. Annales de l'Institut Fourier, Tome 25 (1975) no. 2, pp. 81-126. doi : 10.5802/aif.556. http://www.numdam.org/articles/10.5802/aif.556/

[1] E. Bishop and R.R. Phelps, A proof that every Banach space is subreflexive, Bull. Amer. Math. Soc., 67 (1961), 97-98.

[2] M. Cwikel, On the conjugates of some function space, Studia Math., 45 (1973), 49-55. | MR | Zbl

[3] M. Cwikel, Some results in the Lions-Peetre interpolation theory, Thesis, Weizmann Institute of Science, 1973. | MR | Zbl

[4] M. Cwikel and Y. Sagher, L(p, ∞)*, Indiana Univ. Math. J., 21 (1972), 781-786.

[5] N. Dunford and J.T. Schwartz, Linear Operators, Part I : General Theory, Interscience, New York 1958. | MR | Zbl

[6] R.A. Hunt, On L(p,q) spaces, L'Enseignement Math., 12 (1966), 249-276. | MR | Zbl

[7] R.C. James, Reflexivity and the sup of linear functionals, Israël J. Math., 13 (1972), 289-330. | MR | Zbl

[8] B. Muckenhoupt, Weighted norm inequalities for the Hardy maximal function, Trans. Amer. Math. Soc., 165 (1972), 207-226. | MR | Zbl

  • Pietsch, Albrecht Lorentz spaces depending on more than two parameters, Annals of Functional Analysis, Volume 15 (2024) no. 2 | DOI:10.1007/s43034-023-00313-w
  • Park, Dongjin Global well-posedness and scattering of the defocusing energy-critical inhomogeneous nonlinear Schrödinger equation with radial data, Journal of Mathematical Analysis and Applications, Volume 536 (2024) no. 2, p. 128202 | DOI:10.1016/j.jmaa.2024.128202
  • Formica, Maria Rosaria; Ostrovsky, Eugeny; Sirota, Leonid Connection Between Weighted Tail, Orlicz, Grand Lorentz And Grand Lebesgue Norms, Results in Mathematics, Volume 79 (2024) no. 3 | DOI:10.1007/s00025-024-02136-0
  • Tao, Xiangxing; Zeng, Yuan; Yu, Xiao Boundedness and Compactness for the Commutator of the ω-Type Calderón-Zygmund Operator on Lorentz Space, Acta Mathematica Scientia, Volume 43 (2023) no. 4, p. 1587 | DOI:10.1007/s10473-023-0409-8
  • Karlovych, Oleksiy; Shargorodsky, Eugene On the weak convergence of shift operators to zero on rearrangement-invariant spaces, Revista Matemática Complutense, Volume 36 (2023) no. 1, p. 91 | DOI:10.1007/s13163-022-00423-4
  • Bekjan, Turdebek N.; Raikhan, Madi On noncommutative weak Orlicz–Hardy spaces, Annals of Functional Analysis, Volume 13 (2022) no. 1 | DOI:10.1007/s43034-021-00150-9
  • Karlovych, Oleksiy; Shargorodsky, Eugene Toeplitz Operators with Non-trivial Kernels and Non-dense Ranges on Weak Hardy Spaces, Toeplitz Operators and Random Matrices, Volume 289 (2022), p. 463 | DOI:10.1007/978-3-031-13851-5_20
  • Stolyarov, Dmitriy; Yarcev, Dmitry Fractional integration for irregular martingales, Tohoku Mathematical Journal, Volume 74 (2022) no. 2 | DOI:10.2748/tmj.20210104
  • Karlovich, Alexei Yu. Wavelet Bases in Banach Function Spaces, Bulletin of the Malaysian Mathematical Sciences Society, Volume 44 (2021) no. 3, p. 1669 | DOI:10.1007/s40840-020-01024-4
  • Karlovich, Alexei; Shargorodsky, Eugene Algebras of Convolution Type Operators with Continuous Data do Not Always Contain All Rank One Operators, Integral Equations and Operator Theory, Volume 93 (2021) no. 2 | DOI:10.1007/s00020-021-02631-x
  • Dao, Nguyen Anh; Krantz, Steven G. Lorentz boundedness and compactness characterization of integral commutators on spaces of homogeneous type, Nonlinear Analysis, Volume 203 (2021), p. 112162 | DOI:10.1016/j.na.2020.112162
  • Zhou, Xilin; He, Ziyi; Yang, Dachun Real-Variable Characterizations of Hardy–Lorentz Spaces on Spaces of Homogeneous Type with Applications to Real Interpolation and Boundedness of Calderón–Zygmund Operators, Analysis and Geometry in Metric Spaces, Volume 8 (2020) no. 1, p. 182 | DOI:10.1515/agms-2020-0109
  • HUANG, JINGHAO; LEVITINA, GALINA; SUKOCHEV, FEDOR M-embedded symmetric operator spaces and the derivation problem, Mathematical Proceedings of the Cambridge Philosophical Society, Volume 169 (2020) no. 3, p. 607 | DOI:10.1017/s030500411900029x
  • D’Onofrio, Luigi; Sbordone, Carlo; Schiattarella, Roberta Duality and distance formulas in Banach function spaces, Journal of Elliptic and Parabolic Equations, Volume 5 (2019) no. 1, p. 1 | DOI:10.1007/s41808-018-0030-5
  • Kolwicz, Paweł; Leśnik, Karol; Maligranda, Lech Symmetrization, factorization and arithmetic of quasi-Banach function spaces, Journal of Mathematical Analysis and Applications, Volume 470 (2019) no. 2, p. 1136 | DOI:10.1016/j.jmaa.2018.10.054
  • Karlovich, Alexei; Shargorodsky, Eugene The Brown–Halmos theorem for a pair of abstract Hardy spaces, Journal of Mathematical Analysis and Applications, Volume 472 (2019) no. 1, p. 246 | DOI:10.1016/j.jmaa.2018.11.022
  • LIU, Jun; YANG, Dachun; YUAN, Wen Littlewood-Paley characterizations of anisotropic Hardy-Lorentz spaces, Acta Mathematica Scientia, Volume 38 (2018) no. 1, p. 1 | DOI:10.1016/s0252-9602(17)30115-7
  • Sawano, Yoshihiro; El‐Shabrawy, Saad R. Weak Morrey spaces with applications, Mathematische Nachrichten, Volume 291 (2018) no. 1, p. 178 | DOI:10.1002/mana.201700001
  • Castillo, René Erlín; Rafeiro, Humberto Convex Functions and Inequalities, An Introductory Course in Lebesgue Spaces (2016), p. 1 | DOI:10.1007/978-3-319-30034-4_1
  • Castillo, René Erlín; Rafeiro, Humberto Lorentz Spaces, An Introductory Course in Lebesgue Spaces (2016), p. 215 | DOI:10.1007/978-3-319-30034-4_6
  • Castillo, René Erlín; Rafeiro, Humberto Interpolation of Operators, An Introductory Course in Lebesgue Spaces (2016), p. 313 | DOI:10.1007/978-3-319-30034-4_8
  • Castillo, René Erlín; Rafeiro, Humberto Maximal Operator, An Introductory Course in Lebesgue Spaces (2016), p. 331 | DOI:10.1007/978-3-319-30034-4_9
  • Castillo, René Erlín; Rafeiro, Humberto Integral Operators, An Introductory Course in Lebesgue Spaces (2016), p. 359 | DOI:10.1007/978-3-319-30034-4_10
  • Castillo, René Erlín; Rafeiro, Humberto Convolution and Potentials, An Introductory Course in Lebesgue Spaces (2016), p. 383 | DOI:10.1007/978-3-319-30034-4_11
  • Castillo, René Erlín; Rafeiro, Humberto Lebesgue Spaces, An Introductory Course in Lebesgue Spaces (2016), p. 43 | DOI:10.1007/978-3-319-30034-4_3
  • Liu, Jun; Yang, DaChun; Yuan, Wen Anisotropic Hardy-Lorentz spaces and their applications, Science China Mathematics, Volume 59 (2016) no. 9, p. 1669 | DOI:10.1007/s11425-016-5157-y
  • Grafakos, Loukas L p Spaces and Interpolation, Classical Fourier Analysis, Volume 249 (2014), p. 1 | DOI:10.1007/978-1-4939-1194-3_1
  • Ho, Kwok‐Pun Sobolev‐Jawerth embedding of Triebel‐Lizorkin‐Morrey‐Lorentz spaces and fractional integral operator on Hardy type spaces, Mathematische Nachrichten, Volume 287 (2014) no. 14-15, p. 1674 | DOI:10.1002/mana.201300217
  • Sarkar, Rudra P. Chaotic dynamics of the heat semigroup on the Damek-Ricci spaces, Israel Journal of Mathematics, Volume 198 (2013) no. 1, p. 487 | DOI:10.1007/s11856-013-0035-6
  • Han, Yazhou; Shao, Jingjing The dual of Lp,∞(M), Journal of Mathematical Analysis and Applications, Volume 398 (2013) no. 2, p. 814 | DOI:10.1016/j.jmaa.2012.08.064
  • Liu, PeiDe; Wang, MaoFa Weak Orlicz spaces: Some basic properties and their applications to harmonic analysis, Science China Mathematics, Volume 56 (2013) no. 4, p. 789 | DOI:10.1007/s11425-012-4452-5
  • Capone, Claudia; Formica, Maria Rosaria A Decomposition of the Dual Space of Some Banach Function Spaces, Journal of Function Spaces and Applications, Volume 2012 (2012), p. 1 | DOI:10.1155/2012/737534
  • Arnold, Anton; Kim, JinMyong; Yao, Xiaohua Estimates for a class of oscillatory integrals and decay rates for wave-type equations, Journal of Mathematical Analysis and Applications, Volume 394 (2012) no. 1, p. 139 | DOI:10.1016/j.jmaa.2012.04.070
  • Yazhou, Han; Bekjan, Turdebek N. The dual of noncommutative Lorentz spaces, Acta Mathematica Scientia, Volume 31 (2011) no. 5, p. 2067 | DOI:10.1016/s0252-9602(11)60382-2
  • Alberico, Angela; Alberico, Teresa; Sbordone, Carlo Planar quasilinear elliptic equations with right-hand side in L(logL)δ, Discrete Continuous Dynamical Systems - A, Volume 31 (2011) no. 4, p. 1053 | DOI:10.3934/dcds.2011.31.1053
  • Ning, Liu; Yonggang, Ye Weak Orlicz space and its convergence theorems, Acta Mathematica Scientia, Volume 30 (2010) no. 5, p. 1492 | DOI:10.1016/s0252-9602(10)60141-5
  • Martín, Joaquim; Milman, Mario Pointwise symmetrization inequalities for Sobolev functions and applications, Advances in Mathematics, Volume 225 (2010) no. 1, p. 121 | DOI:10.1016/j.aim.2010.02.022
  • Lotz, Heinrich P. Weak convergence in the dual of weak Lp, Israel Journal of Mathematics, Volume 176 (2010) no. 1, p. 209 | DOI:10.1007/s11856-010-0026-9
  • Liu, PeiDe; Hou, YouLiang; Wang, MaoFa Weak Orlicz space and its applications to the martingale theory, Science China Mathematics, Volume 53 (2010) no. 4, p. 905 | DOI:10.1007/s11425-010-0065-z
  • Jiao, Yong; Peng, Lihua Weak type inequalities for vector-valued martingales, Statistics Probability Letters, Volume 80 (2010) no. 13-14, p. 1128 | DOI:10.1016/j.spl.2010.03.007
  • Lotz, Heinrich P. Rearrangement Invariant Continuous Linear Functionals on Weak L1, Positivity, Volume 12 (2008) no. 1, p. 119 | DOI:10.1007/s11117-007-2111-9
  • Kupka, Joseph; Peck, N. Tenney TheL 1 structure of weakL 1, Mathematische Annalen, Volume 269 (1984) no. 2, p. 235 | DOI:10.1007/bf01451421
  • Johnson, R. Application of Carleson measures to partial differential equations and Fourier multiplier problems, Harmonic Analysis, Volume 992 (1983), p. 16 | DOI:10.1007/bfb0069150
  • Kaijser, Sten On Banach modules I, Mathematical Proceedings of the Cambridge Philosophical Society, Volume 90 (1981) no. 3, p. 423 | DOI:10.1017/s0305004100058904

Cité par 44 documents. Sources : Crossref