Divergence of the \((C,1)\) means of \(d\)-dimensional Walsh-Fourier series
type: Item
instance of: scholarly article
title: Divergence of the \((C,1)\) means of \(d\)-dimensional Walsh-Fourier series
zbMATH Open document ID: 0996.40002
DOI: 10.1023/A:1014305614348
published in: Analysis Mathematica
publication date: 2002-10-20T00:00:00Z
review text: The aim of the paper is to demonstrate the sharpness of theorems by \textit{F. Móricz, F. Schipp} and \textit{W. R. Wade} [Trans. Am. Math. Soc. 329, 131-140 (1992; Zbl 0795.42016)] on the a.e. convergence of the double \((C,1)\) means of the Walsh-Fourier series \(\sigma_n f\to f\) for functions \(f\in L\log^+L(I^2)\) where \(I^2\) is the unit square. The existence of a function \(f\in L^1(I^d)\) is proved such that slightly weaker conditions are satisfied (than the orignal conditions of the above theorems) and \(\sigma_n f\to f\) a.e. is not true.
Mathematics Subject Classification ID: 40G05
Mathematics Subject Classification ID: 42C10
zbMATH DE Number: 1817703
zbMATH Keywords: Walsh-Fourier series
zbMATH Keywords: \((C,1)\) mean
author: G. Gát
reviewed by: László Simon
MaRDI profile type: Publication
full work available at URL: a:1014305614348
OpenAlex ID: W1618127111
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description: scientific article; zbMATH DE number 1817703