Khinchin inequality and Banach-Saks type properties in rearrangement-invariant spaces
F. A. Sukochev ; D. Zanin
Studia Mathematica, Tome 192 (2009), p. 101-122 / Harvested from The Polish Digital Mathematics Library
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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=1nξk∥E≤Cnq, where ξkk≥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 exp(Lp), p ≥ 1. We further apply our results to the study of Banach-Saks index sets in r.i. spaces.

Publié le : 2009-01-01
EUDML-ID : urn:eudml:doc:284619 
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F. A. Sukochev; D. Zanin. Khinchin inequality and Banach-Saks type properties in rearrangement-invariant spaces. Studia Mathematica, Tome 192 (2009) pp. 101-122. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm191-2-1/