Abstract <p> In this paper, we establish some necessary and sufficient conditions for the boundedness of <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12607_2025_1117_Article_IEq1.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(p\)</EquationSource> </InlineEquation>-adic Hardy-Cesàro operators <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12607_2025_1117_Article_IEq3.gif" Format="GIF" Height="23" Rendition="HTML" Resolution="72" Type="Linedraw" Width="31" /> </InlineMediaObject> <EquationSource Format="TEX">\(U_{\psi,s}^p\)</EquationSource> </InlineEquation> on the grand central Morrey spaces <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12607_2025_1117_Article_IEq4.gif" Format="GIF" Height="26" Rendition="HTML" Resolution="72" Type="Linedraw" Width="69" /> </InlineMediaObject> <EquationSource Format="TEX">\({\dot{M}}^{q), \ell}_{\theta}(\mathbb Q^n_p)\)</EquationSource> </InlineEquation>, the grand Herz spaces <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12607_2025_1117_Article_IEq5.gif" Format="GIF" Height="26" Rendition="HTML" Resolution="72" Type="Linedraw" Width="78" /> </InlineMediaObject> <EquationSource Format="TEX">\({\dot{K}}^{\alpha, \ell),\theta}_{q}(\mathbb Q^n_p)\)</EquationSource> </InlineEquation>, and grand Morrey-Herz spaces <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12607_2025_1117_Article_IEq6.gif" Format="GIF" Height="29" Rendition="HTML" Resolution="72" Type="Linedraw" Width="99" /> </InlineMediaObject> <EquationSource Format="TEX">\({M\mathop{K}\limits^.}^{\alpha,\ell),\theta}_{\lambda, q}(\mathbb Q^n_p)\)</EquationSource> </InlineEquation>. </p>

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Hardy-Cesàro Operators on \(p\)-Adic Grand Morrey-Herz Spaces

  • N. T. Hong,
  • K. H. Dung

摘要

Abstract

In this paper, we establish some necessary and sufficient conditions for the boundedness of \(p\) -adic Hardy-Cesàro operators \(U_{\psi,s}^p\) on the grand central Morrey spaces \({\dot{M}}^{q), \ell}_{\theta}(\mathbb Q^n_p)\) , the grand Herz spaces \({\dot{K}}^{\alpha, \ell),\theta}_{q}(\mathbb Q^n_p)\) , and grand Morrey-Herz spaces \({M\mathop{K}\limits^.}^{\alpha,\ell),\theta}_{\lambda, q}(\mathbb Q^n_p)\) .