The martingale Hardy type inequality for Marcinkiewicz-Fejér means of two-dimensional conjugate Walsh-Fourier series
type: Item
instance of: scholarly article
title: The martingale Hardy type inequality for Marcinkiewicz-Fejér means of two-dimensional conjugate Walsh-Fourier series
zbMATH Open document ID: 1282.42026
author: Ushangi Goginava
publication date: 2013-07-16T00:00:00Z
review text: The author proves that the operator \(\tilde{\sigma}_n^{(t)}\) of the Marcinkiewicz-Fejér means of the two-dimensional conjugate Walsh-Fourier series is not uniformly bounded from the Hardy space \(H_p(G\times G)\) to the space \(L_p(G\times G)\), when \(0<p<2/3\). This result approves the conjecture made by Weisz, which states that for the uniform boundedness of the operator \(\tilde{\sigma}_n^{(t)}\) from the Hardy space \(H_p(G\times G)\) to the space \(L_p(G\times G)\), the assumption \(p>2/3\) is essential.
Mathematics Subject Classification ID: 42C10
Mathematics Subject Classification ID: 42B05
Mathematics Subject Classification ID: 42A50
zbMATH DE Number: 6188434
zbMATH Keywords: two-dimensional Walsh-Fourier series
zbMATH Keywords: martingale Hardy space
zbMATH Keywords: Marcinkiewicz-Fejér means
MaRDI profile type: Publication
full work available at URL: s10114-011-9551-7
OpenAlex ID: W2397597215
cites work: Q5773701
cites work: Convergence of double Walsh-Fourier series and Hardy spaces
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cites work: Q3997391
cites work: Q4692472
cites work: Q5457569
DOI: 10.1007/S10114-011-9551-7
published in: Acta Mathematica Sinica, English Series
description: scientific article; zbMATH DE number 6188434