Geodesic
On a~property of the Rademacher system and~$\Lambda(2)$-spaces
Sbornik. Mathematics, Tome 215 (2024) no. 3, pp. 291-307

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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/