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<p>We prove Boas type equivalence results connecting functions from generalized Lipschitz spaces with behavior of its Fourier-Dunkl coefficients. Sufficient condition for generalized absolute convergence of Fourier–Dunkl series is obtained in terms of generalized modulus of smoothness in <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="9_2025_2900_Article_IEq1.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="80" /> </InlineMediaObject> <EquationSource Format="TEX">\(L^2([-\,1,1])\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>L</mi> <mn>2</mn> </msup> <mrow> <mo stretchy="false">(</mo> <mrow> <mo stretchy="false">[</mo> <mo>-</mo> <mspace width="0.166667em" /> <mn>1</mn> <mo>,</mo> <mn>1</mn> <mo stretchy="false">]</mo> </mrow> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> with power weight and its sharpness is established. Also, an inverse approximation theorem and a discrete analogue of classical Titchmarsh equivalence theorem are proved in the Fourier–Dunkl setting.</p>

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Boas Equivalence Results and Conditions for Generalized Absolute Convergence of Fourier–Dunkl Series

  • 期刊论文

  • 发表日期：

    2025年7月5日

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  • Sergey Volosivets

摘要

We prove Boas type equivalence results connecting functions from generalized Lipschitz spaces with behavior of its Fourier-Dunkl coefficients. Sufficient condition for generalized absolute convergence of Fourier–Dunkl series is obtained in terms of generalized modulus of smoothness in \(L^2([-\,1,1])\) L 2 ( [ - 1 , 1 ] ) with power weight and its sharpness is established. Also, an inverse approximation theorem and a discrete analogue of classical Titchmarsh equivalence theorem are proved in the Fourier–Dunkl setting.