Khinchin inequality and Banach-Saks type properties in rearrangement-invariant spaces

Details Khinchin inequality and Banach-Saks type properties in rearrangement-invariant spaces Khinchin inequality and Banach-Saks type properties in rearrangement-invariant spaces

2010-01-14

arxiv.org/abs/1001.2432v1

Studia Math. 191 (2009), no. 2, 101--122

Mathematics

Functional Analysis

Scientific paper

{\it We study the class of all rearrangement-invariant (=r.i.) function spaces $E$ on $[0,1]$ such that there exists $00$ does not depend on $n$. We completely characterize all Lorentz spaces having this property and complement classical results of Rodin and Semenov for Orlicz spaces $exp(L_p)$, $p\ge 1$. We further apply our results to the study of Banach-Saks index sets in r.i. spaces.

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