Approximation by Nörlund means of double Walsh-Fourier series for Lipschitz functions
type: Item
instance of: scholarly article
zbMATH Open document ID: 1243.42038
publication date: 2012-05-23T00:00:00Z
Mathematics Subject Classification ID: 42C10
Mathematics Subject Classification ID: 42B08
zbMATH DE Number: 6037637
zbMATH Keywords: Walsh group
zbMATH Keywords: Walsh system
zbMATH Keywords: Nörlund means
author: Károly Nagy
MaRDI profile type: Publication
full work available at URL: mia-15-25
OpenAlex ID: W2319446472
DOI: 10.7153/MIA-15-25
title: Approximation by Nörlund means of double Walsh-Fourier series for Lipschitz functions
published in: Mathematical Inequalities \& Applications
review text: The Nörlund means of rectangular partial sums of a double Walsh-Fourier series are defined by NEWLINE\[NEWLINE T_{m,n}\left( f;x^{1},x^{2}\right) :=\frac{1}{Q_{m,n}}\sum_{j=0}^{m} \sum_{k=0}^{n}q_{m-j,n-k}S_{j,k}\left( f;x^{1},x^{2}\right) , NEWLINE\]NEWLINE where NEWLINE\[NEWLINE Q_{m,n}:=\sum_{j=0}^{m}\sum_{k=0}^{n}q_{j,k}. NEWLINE\]NEWLINE The main aim of this paper is to investigate the rate of approximation by the Nörlund means \(T_{m,n}\left( f;x^{1},x^{2}\right) \) the double Walsh-Fourier series of a function in \(L_{p},1\leq p\leq \infty \).NEWLINENEWLINEEarlier results on one-dimensional Nörlund means of the Walsh-Fourier series were given by \textit{F. Móricz} and \textit{A. H. Siddiqi} [J. Approximation Theory 70, No. 3, 375--389 (1992; Zbl 0757.42009)].
reviewed by: Ushangi Goginava
description: scientific article; zbMATH DE number 6037637