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A generalized Khintchine inequality in rearrangement invariant spaces

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Abstract

Let X be a separable or maximal rearrangement invariant space on [0, 1]. Necessary and sufficient conditions are found under which the generalized Khintchine inequality

$$\left\| {\sum\limits_{k = 1}^\infty {f_k } } \right\|_X \leqslant C\left\| {\left( {\sum\limits_{k = 1}^\infty {f_k^2 } } \right)^{1/2} } \right\|_X $$

holds for an arbitrary sequence {ƒk} ∞ k=1 ⊂ X of mean zero independent variables. Moreover, the subspace spanned in a rearrangement invariant space by the Rademacher system with independent vector coefficients is studied.

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Authors and Affiliations

  1. Samara State University, Russia

    S. V. Astashkin

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  1. S. V. Astashkin
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Correspondence to S. V. Astashkin.

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__________

Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 42, No. 2, pp. 78–81, 2008

Original Russian Text Copyright © by S. V. Astashkin

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Astashkin, S.V. A generalized Khintchine inequality in rearrangement invariant spaces. Funct Anal Its Appl 42, 144–147 (2008). https://doi.org/10.1007/s10688-008-0021-7

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  • DOI: https://doi.org/10.1007/s10688-008-0021-7

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