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Abstract <p>In this study, we establish order relations for the deviations of functions <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11957_2025_7230_Article_IEq1.gif" Format="GIF" Height="23" Rendition="HTML" Resolution="72" Type="Linedraw" Width="87" /> </InlineMediaObject> <EquationSource Format="TEX">\(f\in H_{p}^{\omega}[\mathbb{T}^{N}]\)</EquationSource> <!--ContMath2460178Patel-m1--> </InlineEquation> by examining the partial sums of their multiple Fourier series within a generalized Hölder metric. Additionally, we obtain the strong approximation properties of multiple Fourier series for functions in the generalized Hölder class <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11957_2025_7230_Article_IEq2.gif" Format="GIF" Height="23" Rendition="HTML" Resolution="72" Type="Linedraw" Width="55" /> </InlineMediaObject> <EquationSource Format="TEX">\(H_{p}^{\omega}[\mathbb{T}^{N}]\)</EquationSource> <!--ContMath2460178Patel-m2--> </InlineEquation>.</p>

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On Groups of Deviations of the Multiple Fourier Series in Generalized Hölder Class

  • 期刊论文

  • 发表日期：

    2025年8月26日

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  • Y. Patel,
  • R. Vyas

摘要

Abstract

In this study, we establish order relations for the deviations of functions \(f\in H_{p}^{\omega}[\mathbb{T}^{N}]\) by examining the partial sums of their multiple Fourier series within a generalized Hölder metric. Additionally, we obtain the strong approximation properties of multiple Fourier series for functions in the generalized Hölder class \(H_{p}^{\omega}[\mathbb{T}^{N}]\) .