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Abstract <p> Weighted Hardy-type inequalities with additional terms are considered. Weight functions depend on the distance function to the boundary of the domain and on the Bessel function. We prove one-dimensional inequalities and their spatial analogs in the <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11006_2025_3084_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">\(L_1\)</EquationSource> </InlineEquation>- and <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11006_2025_3084_Article_IEq2.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">\(L_p\)</EquationSource> </InlineEquation>-cases. As a consequence, we obtain bounds for the strong and weak Hardy constants. </p>

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Hardy’s Constants-Functionals in Inequalities with Additional Summands

  • 期刊论文

  • 发表日期：

    2025年6月1日

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  • R. V. Makarov,
  • R. G. Nasibullin

摘要

Abstract

Weighted Hardy-type inequalities with additional terms are considered. Weight functions depend on the distance function to the boundary of the domain and on the Bessel function. We prove one-dimensional inequalities and their spatial analogs in the \(L_1\) - and \(L_p\) -cases. As a consequence, we obtain bounds for the strong and weak Hardy constants.