A classification of martingale Hardy spaces associated with rearrangement-invariant function spaces期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

按检索

A classification of martingale Hardy spaces associated with rearrangement-invariant function spaces

Authors:	Email author" target="_blank">M?Kikuchi Email author

Institution:	(1) Department of Mathematics, Toyama University, Gofuku 3190, 930-8555 Toyama, Japan

Abstract:	Let X be a rearrangement-invariant Banach function space over a complete probability space $(\Omega,\,\Sigma,\,\mathbb{P})$ , and denote by $\mathbb{H}(X,\,({\cal F}_n))$ the Hardy space consisting of all martingales $f = (f_{n},\, {\cal F}_{n})_{n \geq 0}$ such that $\sup\limits_{n \geq 0} \|f_n\| \in X$ . We prove that $f = (f_{n},\, {\cal F}_n) \in \mathbb{H}(X,\,({\cal F}_n))$ implies ${\cal A}f = ({\cal A}f_{n},\, {\cal F}_n) \in \mathbb{H}(X,\,({\cal F}_n))$ for any filtration ${\cal F} = ({\cal F}_n)$ if and only if Doobs inequality holds in X, where ${\cal A}f = ({\cal A}f_{n},\, {\cal F}_n)$ denotes the martingale defined by ${\cal A}f_{n} = \mathbb{E}\|f_{\infty}\| \, \|{\cal F}_n]$ , n = 0, 1, 2, ..., and $f_{\infty} = \lim\limits_{n \to \infty} f_n$ a.s.Received: 1 August 2000

Keywords:	60G42 60G46 46E30
本文献已被 SpringerLink 等数据库收录！