Remarks on the convergence (boundedness) in the mean of partial sums of a trigonometric series
type: Item
instance of: scholarly article
title: Remarks on the convergence (boundedness) in the mean of partial sums of a trigonometric series
zbMATH Open document ID: 1026.42010
DOI: 10.1023/A:1015860510199
published in: Mathematical Notes
publication date: 2003-06-15T00:00:00Z
review text: This is a worthy paper with respectable results. The author gives fairly general conditions on the coefficients \(\{a_n\}\) of even and odd trigonometric Fourier series under which \(L\)-convergence (boundedness) of partial sums of the series is equivalent to the relation \[ \sum^{2n}_{k= [n/2]}|a_k|/(|n-k|+ 1)= o(1)\qquad (O(1),\text{ respectively}). \] {}.
Mathematics Subject Classification ID: 42A20
Mathematics Subject Classification ID: 42A24
zbMATH DE Number: 1928219
zbMATH Keywords: convergence
zbMATH Keywords: boundedness
zbMATH Keywords: trigonometric Fourier series
zbMATH Keywords: partial sums
author: A. S. Belov
reviewed by: László Leindler
MaRDI profile type: Publication
full work available at URL: a:1015860510199
OpenAlex ID: W57128484
description: scientific article; zbMATH DE number 1928219