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<p>In this paper we give a version of Harris’ criterion for determining <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="20_2025_2794_Article_IEq1.gif" Format="GIF" Height="22" Rendition="HTML" Resolution="72" Type="Linedraw" Width="33" /> </InlineMediaObject> <EquationSource Format="TEX">\(H^{1,p}_0\)</EquationSource> <EquationSource Format="MATHML"><math> <msubsup> <mi>H</mi> <mn>0</mn> <mrow> <mn>1</mn> <mo>,</mo> <mi>p</mi> </mrow> </msubsup> </math></EquationSource> </InlineEquation> within <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="20_2025_2794_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="33" /> </InlineMediaObject> <EquationSource Format="TEX">\(H^{1,p}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>H</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>p</mi> </mrow> </msup> </math></EquationSource> </InlineEquation> on discrete spaces. Moreover, we provide a converse via Hardy inequalities involving distances to metric boundaries.</p>

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Harris’ Criterion and Hardy Inequalities on Graphs

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年3月7日

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  • Simon Murmann,
  • Marcel Schmidt

摘要

In this paper we give a version of Harris’ criterion for determining \(H^{1,p}_0\) H 0 1 , p within \(H^{1,p}\) H 1 , p on discrete spaces. Moreover, we provide a converse via Hardy inequalities involving distances to metric boundaries.