1School of Mathematics and Statistics University of New South Wales Kensington, NSW 2052, Australia 2School of Computer Science Engineering and Mathematics Flinders University Bedford Park, SA 5042, Australia
Studia Mathematica, Tome 191 (2009) no. 2, pp. 101-122
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.
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
Affiliations des auteurs :
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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author = {F. A. Sukochev and D. Zanin},
title = {Khinchin inequality and {Banach{\textendash}Saks} type properties
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journal = {Studia Mathematica},
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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
