Characterization of Banach function spaces that preserve the Burkholder square-function inequality
type: Item
instance of: scholarly article
title: Characterization of Banach function spaces that preserve the Burkholder square-function inequality
zbMATH Open document ID: 1029.60031
author: Masato Kikuchi
published in: Illinois Journal of Mathematics
publication date: 2003-10-16T00:00:00Z
review text: The author considers Banach function space \(X\) over a nonatomic probability space. It is proved that the quadratic function of the uniformly integrable martingale \(f\) is equivalent to \(\lim_{n\to \infty}f_n \) if and only if the space \(X\) is rearrangement-invariant and can be renormed with an equivalent rearrangement-invariant norm satisfying some restrictions on its Boyd indices.
Mathematics Subject Classification ID: 60G42
Mathematics Subject Classification ID: 60G46
Mathematics Subject Classification ID: 46E30
zbMATH DE Number: 1993668
zbMATH Keywords: Burkholder square-function inequality
zbMATH Keywords: uniformly integrable martingale
zbMATH Keywords: Shimogaki theorem
reviewed by: Yuliya S. Mishura
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1993668