Geodesic
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/}
}
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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/