Geodesic
Khinchin inequality and Banach–Saks type properties in rearrangement-invariant spaces
F. A. Sukochev 1   ; D. Zanin 2
1 School of Mathematics and Statistics University of New South Wales Kensington, NSW 2052, Australia
2 School of Computer Science Engineering and Mathematics Flinders University Bedford Park, SA 5042, Australia
Studia Mathematica, Tome 191 (2009) no. 2, pp. 101-122 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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 $ \Vert \sum_{k=1}^n\xi_k\Vert _{E}\leq Cn^{q}$, where $\{\xi_k\}_{k\ge 1}\subset E$ 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 $\exp(L_p)$, $p\ge 1$. We further apply our results to the study of Banach–Saks index sets in r.i. spaces.
DOI : 10.4064/sm191-2-1
Keywords: study class rearrangement invariant function spaces there exists which vert sum vert leq where subset arbitrary sequence independent identically distributed symmetric random variables does depend completely characterize lorentz spaces having property complement classical results rodin semenov orlicz spaces exp further apply results study banach saks index sets spaces

F. A. Sukochev  1   ; D. Zanin  2

1 School of Mathematics and Statistics University of New South Wales Kensington, NSW 2052, Australia
2 School of Computer Science Engineering and Mathematics Flinders University Bedford Park, SA 5042, Australia 
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     title = {Khinchin inequality and {Banach{\textendash}Saks} type properties
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F. A. Sukochev; D. Zanin. Khinchin inequality and Banach–Saks type properties
 in rearrangement-invariant spaces. Studia Mathematica, Tome 191 (2009) no. 2, pp. 101-122. doi: 10.4064/sm191-2-1

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