no. 3
Generalized Lévy representation of norms and isometric embeddings into L p -spaces
Annales de l'I.H.P. Probabilités et statistiques, Tome 28 (1992) no. 3, pp. 335-353. 
@article{AIHPB_1992__28_3_335_0,
     author = {Koldobsky, Alexander L.},
     title = {Generalized {L\'evy} representation of norms and isometric embeddings into $L_p$-spaces},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {335--353},
     publisher = {Gauthier-Villars},
     volume = {28},
     number = {3},
     year = {1992},
     mrnumber = {1183989},
     zbl = {0766.46009},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_1992__28_3_335_0/}
}
TY  - JOUR
AU  - Koldobsky, Alexander L.
TI  - Generalized Lévy representation of norms and isometric embeddings into $L_p$-spaces
JO  - Annales de l'I.H.P. Probabilités et statistiques
PY  - 1992
SP  - 335
EP  - 353
VL  - 28
IS  - 3
PB  - Gauthier-Villars
UR  - http://www.numdam.org/item/AIHPB_1992__28_3_335_0/
LA  - en
ID  - AIHPB_1992__28_3_335_0
ER  - 
%0 Journal Article
%A Koldobsky, Alexander L.
%T Generalized Lévy representation of norms and isometric embeddings into $L_p$-spaces
%J Annales de l'I.H.P. Probabilités et statistiques
%D 1992
%P 335-353
%V 28
%N 3
%I Gauthier-Villars
%U http://www.numdam.org/item/AIHPB_1992__28_3_335_0/
%G en
%F AIHPB_1992__28_3_335_0
Koldobsky, Alexander L. Generalized Lévy representation of norms and isometric embeddings into $L_p$-spaces. Annales de l'I.H.P. Probabilités et statistiques, Tome 28 (1992) no. 3, pp. 335-353. http://www.numdam.org/item/AIHPB_1992__28_3_335_0/

[1] J. Bretagnolle, D. Dacunha-Castelle and J.L. Krivine, Lois stables et spaces Lp, Ann. Inst. H. Poincaré. Ser. B., Vol. 2, 1966, pp. 231-259. | Numdam | MR | Zbl

[2] L. Dor, Potentials and Isometric Embeddings in L1, Israel J. Math., Vol. 24, 1976, pp. 260-268. | MR | Zbl

[3] M.V. Fedoryuck, Assymptotics. Integrals, series, Nauka, Moscow, 1987.

[4] T.S. Ferguson, A Representation of the Symmetric Bivariate Cauchy Distribution, Ann. Math. Stat., Vol. 33, 1962, pp. 1256-1266. | MR | Zbl

[5] M. Frechet, Sur la définition axiomatique d'une classe d'espaces vectoriel distances applicables vectoriellement sur l'espace de Hilbert, Ann. Math., Vol. 36, 1935, pp. 705- 718. | MR | Zbl

[6] I.M. Gelfand and G.E. Shilov, Generalized functions I, Fizmatgiz, Moscow, 1959.

[7] I.M. Gelfand, M.I. Graev and N.Ya. Vilenkin, Generalized Functions 5, Academic Press, New York, 1966. | Zbl

[8] E.A. Gorin and A.L. Koldobsky, On Potentials of Measures in Banach Spaces, Siberian Math. J., Vol. 28, 1987, pp. 46-58. | MR | Zbl

[9] R. Grzaslewicz, Plane Sections of the Unit Ball of Lp, Acta Math. Hung., Vol. 52, 1988, pp. 219-225. | MR | Zbl

[10] C.S. Herz, A Class of Negative Definite Functions, Proc. Am. Math. Soc., Vol. 14, 1963, pp. 670-676. | MR | Zbl

[11] W.B. Johnson, B. Maurey, G. Schechtman and L. Tzafriri, Symmetric structures in Banach spaces, Memoires of the Am. Math. Soc., Vol. 217, 1979, 298 p. | MR | Zbl

[12] P. Jordan and J. Von Neumann, On Inner Products Linear Metric Spaces, Ann. Math., Vol. 36, 1935, pp. 719-723. | JFM

[13] M. Kanter, The Lp-norm of Sums of Translates of a Function, Trans. Am. Math. Soc., Vol. 179, 1973, pp. 35-47. | MR | Zbl

[14] A.L. Koldobsky, Schoenberg's Problem on Positive Definite Functions, Algebra & Analysis, Leningrad Math. J., Vol. 3, No. 3, 1991, pp. 78-85. | Zbl

[15] A.L. Koldobsky, A Formula for the Fourier Transform of Maximum Dependent Functions, preprint.

[16] A.L. Koldobsky, The Fourier Transform Technique for Convolution Equations in Infinite Dimensional lq-spaces, Math. Ann., Vol. 291, 1991, pp. 403-407. | MR | Zbl

[17] A.L. Koldosky, Convolution Equations in Certain Banach Spaces, Proc. Am. Math. Soc., Vol. 111, 1991, pp. 755-765. | Zbl

[18] J.L. Krivine, Plongment des espaces normes dans les Lp pour p > 2, C. R. Acad. Sci. Paris, T. 261, 1965, pp. 4307-4310. | MR | Zbl

[19] Yu.G. Kuritsyn, Multidimensional Versions and Two Schoenberg's Problems, Stability Problems for Stochastic Models, Moscow, 1989, pp. 72-79 (Russian).

[20] P. Levy, Théorie de l'addition de variable aléatoires, Gauthier-Villars, Paris, 1937. | JFM | Zbl

[21] W. Linde, Infinitely Divisible and Stable Measures on Banach Spaces, Teubner-Texte für Mathematik, Vol. 58, Teubner, Leipgiz, 1983. | MR | Zbl

[22] W. Linde, Moments of Measures on Banach Spaces, Math. Ann., Vol. 258, 1982, pp. 277-287. | MR | Zbl

[23] J. Lindenstrauss, On the Extension of Operators with Finite Dimensional Range,Illinois J. Math., Vol. 8, 1964, pp. 488-499. | MR | Zbl

[24] J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces, Lect. Notes Math., Vol. 338, 1973. | MR | Zbl

[25] J. Misiewicz, On Norm Dependent Positive Definite Functions, Bull. Acad. Sci. Georgian SSR, Vol. 130, 1988, pp. 253-256 (Russian). | MR | Zbl

[26] J. Misiewicz, Positive Definite Functions on l∞, Statist. and Probab. Lett., Vol. 8, 1989, pp. 255-260. | MR | Zbl

[27] A. Neyman, Representation of Lp-Norms and Isometric Embedding in Lp-Spaces, Israel J. Math., Vol. 48, 1984, pp. 129-138. | MR | Zbl

[28] G. Polya, On the Zeroes of an Integral Function Represented by Fourier's Integral, Messenger Math., Vol. 52, 1923, pp. 185-188. | JFM

[29] G. Polya and G. Szego, Aufgaben und lehrsatze aus der analysis, Springer-Verlag, Berlin-New York, 1964.

[30] I.J. Schoenberg, Metric Spaces and Positive Definite Functions, Trans. Am. Math. Soc., Vol. 44, 1938, pp. 522-536. | JFM | MR | Zbl

[31] I.J. Schoenberg, Metric Spaces and Completely Monotone Functions, Ann. Math., Vol. 39, 1938, pp. 811-841. | JFM | MR | Zbl

[32] V.M. Zolotarev, One-Dimensional Stable Distributions, Nauka, Moscow, 1983. | MR | Zbl

[33] D. Yost, L1 Contains Every Two-Dimensional Normed Space, Ann. Polonici Math., Vol. 49, 1988, pp. 17-19. | MR | Zbl

[34] I. Aharoni, B. Maurey and B.S. Mityagin, Uniform Embeddings of Metric Spaces and of Banach Spaces into Hilbert Spaces, Israel J. Math., Vol. 52, 1985, pp. 251- 265. | MR | Zbl