Generalized Levy representation of norms and isometric embeddings into $L_p$-spaces

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1. [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. Zbl0139.33501MR203757
2. [2] L. Dor, Potentials and Isometric Embeddings in L1, Israel J. Math., Vol. 24, 1976, pp. 260-268. Zbl0345.46018MR417756
3. [3] M.V. Fedoryuck, Assymptotics. Integrals, series, Nauka, Moscow, 1987. 
4. [4] T.S. Ferguson, A Representation of the Symmetric Bivariate Cauchy Distribution, Ann. Math. Stat., Vol. 33, 1962, pp. 1256-1266. Zbl0111.33402MR143281
5. [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. Zbl0012.30701MR1503246
6. [6] I.M. Gelfand and G.E. Shilov, Generalized functions I, Fizmatgiz, Moscow, 1959. 
7. [7] I.M. Gelfand, M.I. Graev and N.Ya. Vilenkin, Generalized Functions5, Academic Press, New York, 1966. Zbl0144.17202
8. [8] E.A. Gorin and A.L. Koldobsky, On Potentials of Measures in Banach Spaces, Siberian Math. J., Vol. 28, 1987, pp. 46-58. Zbl0637.46042MR886854
9. [9] R. Grzaslewicz, Plane Sections of the Unit Ball of Lp, Acta Math. Hung., Vol. 52, 1988, pp. 219-225. Zbl0683.52004MR991856
10. [10] C.S. Herz, A Class of Negative Definite Functions, Proc. Am. Math. Soc., Vol. 14, 1963, pp. 670-676. Zbl0178.54102MR158251
11. [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. Zbl0421.46023MR527010
12. [12] P. Jordan and J. Von Neumann, On Inner Products Linear Metric Spaces, Ann. Math., Vol. 36, 1935, pp. 719-723. Zbl61.0435.05JFM61.0435.05
13. [13] M. Kanter, The Lp-norm of Sums of Translates of a Function, Trans. Am. Math. Soc., Vol. 179, 1973, pp. 35-47. Zbl0271.43007MR361617
14. [14] A.L. Koldobsky, Schoenberg's Problem on Positive Definite Functions, Algebra & Analysis, Leningrad Math. J., Vol. 3, No. 3, 1991, pp. 78-85. Zbl0791.60012
15. [15] A.L. Koldobsky, A Formula for the Fourier Transform of Maximum Dependent Functions, preprint. Zbl1055.52003
16. [16] A.L. Koldobsky, The Fourier Transform Technique for Convolution Equations in Infinite Dimensional lq-spaces, Math. Ann., Vol. 291, 1991, pp. 403-407. Zbl0725.47015MR1133339
17. [17] A.L. Koldosky, Convolution Equations in Certain Banach Spaces, Proc. Am. Math. Soc., Vol. 111, 1991, pp. 755-765. Zbl0748.46017
18. [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. Zbl0141.12004MR194870
19. [19] Yu.G. Kuritsyn, Multidimensional Versions and Two Schoenberg's Problems, Stability Problems for Stochastic Models, Moscow, 1989, pp. 72-79 (Russian). 
20. [20] P. Levy, Théorie de l'addition de variable aléatoires, Gauthier-Villars, Paris, 1937. Zbl0016.17003JFM63.0490.04
21. [21] W. Linde, Infinitely Divisible and Stable Measures on Banach Spaces, Teubner-Texte für Mathematik, Vol. 58, Teubner, Leipgiz, 1983. Zbl0526.28011MR758255
22. [22] W. Linde, Moments of Measures on Banach Spaces, Math. Ann., Vol. 258, 1982, pp. 277-287. Zbl0465.46036MR649200
23. [23] J. Lindenstrauss, On the Extension of Operators with Finite DimensionalRange,Illinois J. Math., Vol. 8, 1964, pp. 488-499. Zbl0132.09803MR169062
24. [24] J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces, Lect. Notes Math., Vol. 338, 1973. Zbl0259.46011MR415253
25. [25] J. Misiewicz, On Norm Dependent Positive Definite Functions, Bull. Acad. Sci. Georgian SSR, Vol. 130, 1988, pp. 253-256 (Russian). Zbl0655.42010MR979262
26. [26] J. Misiewicz, Positive Definite Functions on l∞, Statist. and Probab. Lett., Vol. 8, 1989, pp. 255-260. Zbl0691.60012MR1024036
27. [27] A. Neyman, Representation of Lp-Norms and Isometric Embedding in Lp-Spaces, Israel J. Math., Vol. 48, 1984, pp. 129-138. Zbl0599.46047MR770695
28. [28] G. Polya, On the Zeroes of an Integral Function Represented by Fourier's Integral, Messenger Math., Vol. 52, 1923, pp. 185-188. JFM49.0219.02
29. [29] G. Polya and G. Szego, Aufgaben und lehrsatze aus der analysis, Springer-Verlag, Berlin-New York, 1964. Zbl0122.29704
30. [30] I.J. Schoenberg, Metric Spaces and Positive Definite Functions, Trans. Am. Math. Soc., Vol. 44, 1938, pp. 522-536. Zbl0019.41502MR1501980JFM64.0617.02
31. [31] I.J. Schoenberg, Metric Spaces and Completely Monotone Functions, Ann. Math., Vol. 39, 1938, pp. 811-841. Zbl0019.41503MR1503439JFM64.0617.03
32. [32] V.M. Zolotarev, One-DimensionalStable Distributions, Nauka, Moscow, 1983. Zbl0523.60003MR721815
33. [33] D. Yost, L1 Contains Every Two-Dimensional Normed Space, Ann. Polonici Math., Vol. 49, 1988, pp. 17-19. Zbl0679.46016MR985361
34. [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. Zbl0596.46010MR815815