Geodesic
On a property of the Rademacher system and $\Lambda(2)$-spaces
Sbornik. Mathematics, Tome 215 (2024) no. 3, pp. 291-307 Cet article a éte moissonné depuis la source Math-Net.Ru

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The closed linear span of the Rademacher functions in $L^2[0,1]$ contains functions with arbitrarily large distribution, provided that the ratio of this distribution to the distribution of a standard normal variable tends to zero. A similar result is also obtained for some classes of $\Lambda(2)$-spaces. Bibliography: 18 titles.
Keywords: Rademacher system, $L^2$-space, rearrangement invariant space, Orlicz space, independent functions
Mots-clés : $\Lambda(2)$-space. 
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S. V. Astashkin; E. M. Semenov. On a property of the Rademacher system and $\Lambda(2)$-spaces. Sbornik. Mathematics, Tome 215 (2024) no. 3, pp. 291-307. http://geodesic.mathdoc.fr/item/SM_2024_215_3_a0/

[1] A. Zygmund, Trigonometric series, v. 1, 2nd ed., Cambridge Univ. Press, New York, 1959, xii+383 pp. | MR | Zbl

[2] V. A. Rodin and E. M. Semyonov (Semenov), “Rademacher series in symmetric spaces”, Anal. Math., 1:3 (1975), 207–222 | DOI | MR | Zbl

[3] J. Lindenstrauss and L. Tzafriri, Classical Banach spaces, v. II, Ergeb. Math. Grenzgeb., 97, Function spaces, Springer-Verlag, Berlin–New York, 1979, x+243 pp. | MR | Zbl

[4] S. V. Astashkin, The Rademacher system in function spaces, Birkhäuser/Springer, Cham, 2020, xx+559 pp. | DOI | MR | Zbl

[5] S. V. Astashkin and E. M. Semenov, “Spaces defined by the Paley function”, Sb. Math., 204:7 (2013), 937–957 | DOI | MR | Zbl

[6] F. Albiac and N. J. Kalton, Topics in Banach space theory, Grad. Texts in Math., 233, Springer, New York, 2006, xii+373 pp. | DOI | MR | Zbl

[7] W. Rudin, “Trigonometric series with gaps”, J. Math. Mech., 9 (1960), 203–227 | MR | Zbl

[8] J. Bourgain, “Bounded orthogonal systems and the $\Lambda(p)$-set problem”, Acta Math., 162:3–4 (1989), 227–245 | DOI | MR | Zbl

[9] N. N. Vakhania, V. I. Tarieladze and S. A. Chobanyan, Probability distributions on Banach spaces, Math. Appl. (Soviet Ser.), 14, D. Reidel Publishing Co., Dordrecht, 1987, xxvi+482 pp. | DOI | MR | Zbl

[10] S. G. Kreĭn, Ju. I. Petunin and E. M. Semenov, Interpolation of linear operators, Transl. Math. Monogr., 54, Amer. Math. Soc., Providence, RI, 1982, xii+375 pp. | MR | Zbl

[11] C. Bennett and R. Sharpley, Interpolation of operators, Pure Appl. Math., 129, Academic Press, Inc., Boston, MA, 1988, xiv+469 pp. | MR | Zbl

[12] M. A. Krasnosel'skiĭ and Ya. B. Rutickiĭ, Convex functions and Orlicz spaces, P. Noordhoff Ltd., Groningen, 1961, xi+249 pp. | MR | Zbl

[13] M. M. Rao and Z. D. Ren, Theory of Orlicz spaces, Monogr. Textbooks Pure Appl. Math., 146, Marcel Dekker, Inc., New York, 1991, xii+449 pp. | MR | Zbl

[14] C. Bennett, R. A. DeVore and R. Sharpley, “Weak-$L^\infty$ and BMO”, Ann. of Math. (2), 113:3 (1981), 601–611 | DOI | MR | Zbl

[15] A. Korenovskiĭ, Mean oscillations and equimeasurable rearrangements of functions, Lect. Notes Unione Mat. Ital., 4, Springer-Verlag, Berlin–Heidelberg, 2007, viii+188 pp. | DOI | MR | Zbl

[16] B. S. Kashin and A. A. Saakyan, Orthogonal series, 2nd ed., Actuarial and Financial Center, Moscow, 1999, x+550 pp. ; English transl of 1st ed., Transl. Math. Monogr., 75, Amer. Math. Soc., Providence, RI, 1989, xii+451 pp. | MR | Zbl | DOI | MR | Zbl

[17] S. V. Astashkin, “Systems of random variables equivalent in distribution to the Rademacher system and $\mathscr K$-closed representability of Banach couples”, Sb. Math., 191:6 (2000), 779–807 | DOI | MR | Zbl

[18] M. I. Kadec and A. Pełczyński, “Bases, lacunary sequences and complemented subspaces in the spaces $L_{p}$”, Studia Math., 21:2 (1962), 161–176 | DOI | MR | Zbl