Waterman classes and spherical partial sums of double Fourier series
type: Item
instance of: scholarly article
title: Waterman classes and spherical partial sums of double Fourier series
zbMATH Open document ID: 0820.42005
DOI: 10.1007/BF01904022
author: M. I. Dyachenko
published in: Analysis Mathematica
publication date: 1995-09-11T00:00:00Z
review text: Spherical partial sums of the double trigonometric Fourier series of functions \(f\) from Waterman's class \(\Lambda\text{BV}(T^ 2)\) are investigated. It is shown that if \(f(x, y)\in \Lambda_ 0\text{BV}(T^ 2)\), where \(\Lambda_ 0= \{{1\over \sqrt n}\}^ \infty_{n= 1}\), then the spherical partial sums of its Fourier series are uniformly bounded (with respect to both \((x, y)\in T^ 2\)).
Mathematics Subject Classification ID: 42B05
zbMATH DE Number: 746074
zbMATH Keywords: double trigonometric Fourier series
zbMATH Keywords: Waterman class
zbMATH Keywords: spherical partial sums
reviewed by: B. P. Osilenker
MaRDI profile type: Publication
cites work: Some results on double Fourier series
cites work: Q5671134
cites work: Q5640160
cites work: Q5724110
full work available at URL: https://doi.org/10.1007/bf01904022
OpenAlex ID: W50699002
description: scientific article; zbMATH DE number 746074