Marcinkiewicz-Fejér means of \(d\)-dimensional Walsh--Fourier series
type: Item
instance of: scholarly article
title: Marcinkiewicz-Fejér means of \(d\)-dimensional Walsh--Fourier series
zbMATH Open document ID: 1070.42019
author: Ushangi Goginava
published in: Journal of Mathematical Analysis and Applications
publication date: 2005-06-10T00:00:00Z
review text: It is proved that the Marcinkiewicz maximal operator of a \(d\)-dimensional Walsh-Fourier series is bounded from the Hardy-Lorentz space \(H_{p,q}\) to \(L_{p,q}\) \((p>d/(d+1), 0<q\leq \infty)\) and it is of weak type \((1,1)\). From this it follows that the Marcinkiewicz means of a function \(f \in L_1\) converge to \(f\) a.e. All these results can be found for \(d=2\) in [\textit{F. Weisz}, ''Convergence of double Walsh-Fourier series and Hardy spaces''. Approximation Theory Appl. 17, No.~2, 32--44 (2001; Zbl 0992.42013)].
Mathematics Subject Classification ID: 42C10
Mathematics Subject Classification ID: 43A75
Mathematics Subject Classification ID: 42B30
zbMATH DE Number: 2174933
zbMATH Keywords: Hardy spaces
zbMATH Keywords: \(p\)-atom, \(p\)-quasi-local operator
zbMATH Keywords: Walsh-Fourier series
zbMATH Keywords: Marcinkiewicz-Fejér summability
reviewed by: Ferenc Weisz
MaRDI profile type: Publication
full work available at URL: j.jmaa.2004.11.001
OpenAlex ID: W2043727809
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DOI: 10.1016/J.JMAA.2004.11.001
description: scientific article; zbMATH DE number 2174933