A Generalized Khintchine Inequality in Rearrangement Invariant Spaces
Funkcionalʹnyj analiz i ego priloženiâ, Tome 42 (2008) no. 2, pp. 78-81
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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.
@article{FAA_2008_42_2_a9,
author = {S. V. Astashkin},
title = {A {Generalized} {Khintchine} {Inequality} in {Rearrangement} {Invariant} {Spaces}},
journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
pages = {78--81},
publisher = {mathdoc},
volume = {42},
number = {2},
year = {2008},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/FAA_2008_42_2_a9/}
}
S. V. Astashkin. A Generalized Khintchine Inequality in Rearrangement Invariant Spaces. Funkcionalʹnyj analiz i ego priloženiâ, Tome 42 (2008) no. 2, pp. 78-81. http://geodesic.mathdoc.fr/item/FAA_2008_42_2_a9/