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Funktsional'nyi Analiz i ego Prilozheniya, 2008, Volume 42, Issue 2, Pages 78–81
DOI: https://doi.org/10.4213/faa2905 (Mi faa2905) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Brief communications

A Generalized Khintchine Inequality in Rearrangement Invariant Spaces

S. V. Astashkin

Samara State University
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DOI: https://doi.org/10.4213/faa2905
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
\begin{equation*} \bigg\|\sum_{k=1}^\infty f_k\bigg\|_{X}\le C\bigg\|\bigg(\sum_{k=1}^\infty f_k^2\bigg)^{1/2}\bigg\|_X \end{equation*}
holds for an arbitrary sequence $\{f_k\}_{k=1}^\infty\subset X$ of mean zero independent variables. Moreover, the subspace spanned in a rearrangement invariant space by the Rademacher system with independent vector coefficients is studied.
Keywords: Khintchine inequality, rearrangement invariant space, Rademacher system, independent functions, Kruglov property, Boyd indices.
Received: 25.10.2006
English version:
Functional Analysis and Its Applications, 2008, Volume 42, Issue 2, Pages 144–147
DOI: https://doi.org/10.1007/s10688-008-0021-7
Bibliographic databases:
Document Type: Article
UDC: 517.982.27
Language: Russian
Citation: S. V. Astashkin, “A Generalized Khintchine Inequality in Rearrangement Invariant Spaces”, Funktsional. Anal. i Prilozhen., 42:2 (2008), 78–81; Funct. Anal. Appl., 42:2 (2008), 144–147
Citation in format AMSBIB
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Функциональный анализ и его приложения Functional Analysis and Its Applications
     
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