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

F. A. Sukochev, and D. Zanin. "Khinchin inequality and Banach-Saks type properties in rearrangement-invariant spaces." Studia Mathematica 191.2 (2009): 101-122. <http://eudml.org/doc/284619>.

@article{F2009,
abstract = {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 $∥∑_\{k=1\}^\{n\}ξ_\{k\}∥_\{E\} ≤ Cn^\{q\}$, 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 $exp(L_\{p\})$, p ≥ 1. We further apply our results to the study of Banach-Saks index sets in r.i. spaces.},
author = {F. A. Sukochev, D. Zanin},
journal = {Studia Mathematica},
keywords = {-Banach–Saks type properties; rearrangement-invariant spaces; Khinchin inequality; Kruglov property},
language = {eng},
number = {2},
pages = {101-122},
title = {Khinchin inequality and Banach-Saks type properties in rearrangement-invariant spaces},
url = {http://eudml.org/doc/284619},
volume = {191},
year = {2009},
}

TY - JOUR
AU - F. A. Sukochev
AU - D. Zanin
TI - Khinchin inequality and Banach-Saks type properties in rearrangement-invariant spaces
JO - Studia Mathematica
PY - 2009
VL - 191
IS - 2
SP - 101
EP - 122
AB - 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 $∥∑_{k=1}^{n}ξ_{k}∥_{E} ≤ Cn^{q}$, 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 $exp(L_{p})$, p ≥ 1. We further apply our results to the study of Banach-Saks index sets in r.i. spaces.
LA - eng
KW - -Banach–Saks type properties; rearrangement-invariant spaces; Khinchin inequality; Kruglov property
UR - http://eudml.org/doc/284619
ER -