A classification of martingale Hardy spaces associated withrearrangement-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

A classification of martingale Hardy spaces associated withrearrangement-invariant function spaces

Authors:	M.?Kikuchi author-information" > author-information__contact u-icon-before" > mailto:kikuchi@sci.toyama-u.ac.jp" title=" kikuchi@sci.toyama-u.ac.jp" itemprop=" email" data-track=" click" data-track-action=" Email author" data-track-label=" " >Email author

Affiliation:	(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 , 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 $suplimits_{n geq 0} \|f_n\| in X$ . 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 $f_{infty} = limlimits_{n to infty} f_n$ a.s.Received: 1 August 2000

Keywords:	60G42 60G46 46E30
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