Pointwise approximation by partial sums of Fourier series and conjugate series
type: Item
instance of: scholarly article
title: Pointwise approximation by partial sums of Fourier series and conjugate series
zbMATH Open document ID: 0658.42003
author: Paulina Pych-Taberska
published in: Functiones et Approximatio. Commentarii Mathematici
publication date: 1986-01-01T00:00:00Z
review text: \textit{R. Bojanić} [Publ. Inst. Math. Nouv. Sér. 26(40), 57-60, (1979; Zbl 0451.42004)] has found the estimate of the rate of pointwise convergence of the partial sums of the Fourier series for functions of bounded variation. An estimate af a different nature for the rate of uniforme convergence of these sums corresponding to continuous functions was obtained by \textit{Z. A. Chanturiya} [Mat. Sbornik, N. Ser. 100(142), 534-554 (1976; Zbl 0339.42005)]. The aim of this paper is to obtain the pointwise analogue of Chanturiya's inequality and to extend the Bojanić result to the case of Wiener classes \(BV_ p(p>1)\). Some estimates for the rate of convergence of conjugate sums of the partial sums of the Fourier series are also presented.
Mathematics Subject Classification ID: 42A10
zbMATH DE Number: 4075732
zbMATH Keywords: rate of pointwise convergence
zbMATH Keywords: conjugate sums
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4075732