Classification of the isomorphic types of martingale-\(H^ 1\) spaces
type: Item
instance of: scholarly article
title: Classification of the isomorphic types of martingale-\(H^ 1\) spaces
zbMATH Open document ID: 0649.46048
DOI: 10.1007/BF02787261
author: Paul F. X. Müller
published in: Israel Journal of Mathematics
publication date: 1987-01-01T00:00:00Z
review text: Sei \(({\mathcal F}_ n)\) eine wachsende Folge von endlichen Algebren auf dem Wahrscheinlichkeitsraum \((\Omega,{\mathcal F},P)\), wobei \({\mathcal F}\) die von \(\cup_{n}{\mathcal F}_ n\) erzeugte \(\sigma\)-Algebra ist. Dann ist \(H^ 1({\mathcal F}_ n)\) isomorph als Banachraum zu \(H^ 1(\delta)\), \((\sum H^ 1_ n)_{\ell^ 1}\) oder \(\ell^ 1\). Dies beantwortet eine von \textit{B. Maurey} [Acta Math. 145, 79-120 (1980; Zbl 0509.46045)] gestellte Frage. Unter anderem folgt daraus, daß \(H^ 1({\mathcal F}_ n)\) eine unbedingte Basis besitzt.
Mathematics Subject Classification ID: 46J15
Mathematics Subject Classification ID: 42B30
Mathematics Subject Classification ID: 60G42
Mathematics Subject Classification ID: 46E15
Mathematics Subject Classification ID: 46B15
Mathematics Subject Classification ID: 46B20
zbMATH DE Number: 4060116
zbMATH Keywords: martingales
zbMATH Keywords: \(H^ 1\)-spaces
zbMATH Keywords: Hardy-space
zbMATH Keywords: unconditional basis
reviewed by: Gunter Bengel
MaRDI profile type: Publication
cites work: Q3922907
cites work: BMO and the Banach Space Approximation Problem
cites work: Q4136031
cites work: Isomorphismes entre espaces \(H_ 1\)
cites work: Q3833044
cites work: On the span of some three valued martingale difference sequences in \(L^ p\) \((1<p<\infty)\) and \(H^ 1\)
full work available at URL: https://doi.org/10.1007/bf02787261
OpenAlex ID: W2021983555
description: scientific article; zbMATH DE number 4060116