Approximation of integrable functions by general linear operators of their Fourier series at the Lebesgue points

Włodzimierz Łenski; Bogdan Szal

doi:10.1007/s10474-011-0077-3

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Acta Mathematica Hungarica

Volume/Issue:: Volume 131: Issue 4

Approximation of integrable functions by general linear operators of their Fourier series at the Lebesgue points

Authors: Włodzimierz Łenski¹ and Bogdan Szal¹

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¹ Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra, 65-516 Zielona Góra, ul. Szafrana 4a, Poland

DOI:: https://doi.org/10.1007/s10474-011-0077-3

Page Count:: 380–394

Publication Date:: 01 Jun 2011

Online Publication Date:: 02 Mar 2011

Article Category:: Research Article

Article Info

Page Count:: 380–394

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Abstract

Pointwise estimates of the deviation T _n,A,B f(⋅)−f(⋅) in terms of moduli of continuity and w _⋅ f are proved. Analog results on norm approximation with remarks and corollaries are also given. In the results essentially weaker conditions than those in [2, Theorem 1, p. 437] are used.