Martingale transforms between Hardy-Orlicz spaces \(\mathcal 2_{\Phi_1}\) and \(\mathcal 2_{\Phi_2}\) of martingales
type: Item
instance of: scholarly article
title: Martingale transforms between Hardy-Orlicz spaces \(\mathcal 2_{\Phi_1}\) and \(\mathcal 2_{\Phi_2}\) of martingales
zbMATH Open document ID: 1234.60046
author: Lin Yu
published in: Statistics \& Probability Letters
publication date: 2011-07-26T00:00:00Z
review text: It is known that \(f\) is in the Hardy space \(\mathcal{D}_{p_1}\) of martingales with predictable quadratic variation if and only if \(f\) is a martingale transform of a martingale from the space \(\mathcal{D}_{p_2}\), where \(0<p_1<p_2<\infty\) (see [\textit{A. M. Garsia}, Martingale Inequalities. Seminar notes on recent progress. Reading, Mass. etc.: W. A. Benjamin, Inc. Advanced Book Program (1973; Zbl 0284.60046)] and [\textit{F. Weisz}, Martingale Hardy spaces and their applications in Fourier analysis. Berlin: Springer-Verlag (1994; Zbl 0796.60049)]). This theorem is generalized for Hardy-Orlicz spaces of martingales.
Mathematics Subject Classification ID: 60G42
zbMATH DE Number: 5932064
zbMATH Keywords: martingales
zbMATH Keywords: martingale transforms
zbMATH Keywords: martingale Hardy-Orlicz spaces
zbMATH Keywords: predictable quadratic variation
reviewed by: Ferenc Weisz
MaRDI profile type: Publication
full work available at URL: j.spl.2011.02.036
OpenAlex ID: W1983658375
cites work: Martingale Transforms
cites work: Martingale transforms and Hardy spaces
cites work: Q4771939
cites work: Q3339868
cites work: Q3135095
cites work: Martingale transforms between \(\mathcal Q_1\) and \(\mathcal Q_{\varPhi}\) of martingale spaces
cites work: Hardy spaces of predictable martingales
cites work: Martingale Hardy spaces and their applications in Fourier analysis
DOI: 10.1016/J.SPL.2011.02.036
description: scientific article; zbMATH DE number 5932064