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

F. A. Sukochev, D. Zanin (2009)

Studia Mathematica

We study the class of all rearrangement-invariant ( = r.i.) function spaces E on [0,1] such that there exists 0 < q < 1 for which k = 1 n ξ k E C n q , where ξ k k 1 E is an arbitrary sequence of independent identically distributed symmetric random variables on [0,1] and C > 0 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 e x p ( L p ) , p ≥ 1. We further apply our results to the study of Banach-Saks index sets in...

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