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<p>We obtain estimates for the rates of approximation by Riesz-Zyg-mund, Borel and generalized Abel-Poisson means of Fourier series in weighted variable exponent spaces of <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40315_2025_596_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="21" /> </InlineMediaObject> <EquationSource Format="TEX">\(2\pi\)</EquationSource> </InlineEquation>-perodic functions and similar results for Faber series in weighted variable exponent Smirnov space. The equivalence of generalized modulus of smoothness in <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40315_2025_596_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="27" /> </InlineMediaObject> <EquationSource Format="TEX">\(n^{-1}\)</EquationSource> </InlineEquation> and approximation by Riesz-Zygmund means of order <i>n</i> is established in both cases.</p>

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Approximation of Functions by Riesz-Zygmund, Borel and Abel-Poisson Means in Weighted Smirnov Classes with Variable Exponent

  • 期刊论文

  • 发表日期：

    2025年10月6日

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  • Sergey Volosivets

摘要

We obtain estimates for the rates of approximation by Riesz-Zyg-mund, Borel and generalized Abel-Poisson means of Fourier series in weighted variable exponent spaces of \(2\pi\) -perodic functions and similar results for Faber series in weighted variable exponent Smirnov space. The equivalence of generalized modulus of smoothness in \(n^{-1}\) and approximation by Riesz-Zygmund means of order n is established in both cases.