# Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty

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

### Tom 191 / 2009

Studia Mathematica 191 (2009), 101-122 MSC: 46E30, 46B20. DOI: 10.4064/sm191-2-1

#### Streszczenie

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.

#### Autorzy

• F. A. SukochevSchool of Mathematics and Statistics
University of New South Wales
Kensington, NSW 2052, Australia
e-mail
• D. ZaninSchool of Computer Science
Engineering and Mathematics
Flinders University
Bedford Park, SA 5042, Australia
e-mail

## Przeszukaj wydawnictwa IMPAN

Zbyt krótkie zapytanie. Wpisz co najmniej 4 znaki.

Odśwież obrazek