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

• Autorzy: F. A. Sukochev , D. Zanin
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 46B20: Geometry and structure of normed linear spaces
• 46E30: Spaces of measurable functions ( L p -spaces, Orlicz spaces, K\"othe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2009
• Tom: 191
• Numer: 2
• Strony: 101-122

Daty

wydano

2009

Twórcy

autor

F. A. Sukochev

• School of Mathematics and Statistics, University of New South Wales, Kensington, NSW 2052, Australia

autor

D. Zanin

• School of Computer Science, Engineering and Mathematics, Flinders University, Bedford Park, SA 5042, Australia

Identyfikatory

DOI

10.4064/sm191-2-1