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Abstract <p>This paper presents the results on differential properties of the subharmonic functions. It is proved that the Riesz potential <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12202_2025_8189_Article_IEq3.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="59" /> </InlineMediaObject> <EquationSource Format="TEX">\({U_{n-\alpha}^{\mu}(x)}\)</EquationSource> <!--LobJMat2560016Imomkulov-m3--> </InlineEquation> <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12202_2025_8189_Article_IEq4.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="88" /> </InlineMediaObject> <EquationSource Format="TEX">\({(1\leq\alpha&lt;n)}\)</EquationSource> <!--LobJMat2560016Imomkulov-m4--> </InlineEquation> belongs to the Zygmund class under certain sufficient conditions imposed on the measure <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12202_2025_8189_Article_IEq5.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mu\)</EquationSource> <!--LobJMat2560016Imomkulov-m5--> </InlineEquation>.</p>

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\(\boldsymbol{C^{k}}\)-Properties of Subharmonic Functions

  • 期刊论文

  • 发表日期：

    2025年2月1日

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  • S. A. Imomkulov,
  • S. A. Gadaev

摘要

Abstract

This paper presents the results on differential properties of the subharmonic functions. It is proved that the Riesz potential \({U_{n-\alpha}^{\mu}(x)}\) \({(1\leq\alpha<n)}\) belongs to the Zygmund class under certain sufficient conditions imposed on the measure \(\mu\) .