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<p>We prove a criterion for Lipschitz and <i>BMO</i> type boundedness of commutators of a class of operators associated to the Schrödinger operator <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13348_2025_497_Article_IEq1.gif" Format="GIF" Height="15" Rendition="HTML" Resolution="72" Type="Linedraw" Width="95" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathcal {L}=-\Delta +V\)</EquationSource> </InlineEquation>. This result is applied to get endpoint boundedness of Riesz transforms and fractional integrals associated to <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13348_2025_497_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathcal {L}\)</EquationSource> </InlineEquation>.</p>

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Lipschitz and BMO type boundedness for commutators of Schrödinger operators

  • 期刊论文

  • 发表日期：

    2025年11月1日

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  • Oscar Salinas,
  • Beatriz Viviani

摘要

We prove a criterion for Lipschitz and BMO type boundedness of commutators of a class of operators associated to the Schrödinger operator \(\mathcal {L}=-\Delta +V\) . This result is applied to get endpoint boundedness of Riesz transforms and fractional integrals associated to \(\mathcal {L}\) .