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<p>In this paper we prove the boundedness of the generalized fractional integral operator <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13324_2025_1091_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="16" /> </InlineMediaObject> <EquationSource Format="TEX">\(I_{\rho }\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>I</mi> <mi>ρ</mi> </msub> </math></EquationSource> </InlineEquation> on generalized Morrey spaces with variable growth condition, which is an improvement of previous results, and then, we establish the boundedness of <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13324_2025_1091_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="16" /> </InlineMediaObject> <EquationSource Format="TEX">\(I_{\rho }\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>I</mi> <mi>ρ</mi> </msub> </math></EquationSource> </InlineEquation> on their bi-preduals. We also prove the boundedness of <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13324_2025_1091_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="16" /> </InlineMediaObject> <EquationSource Format="TEX">\(I_{\rho }\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>I</mi> <mi>ρ</mi> </msub> </math></EquationSource> </InlineEquation> on their preduals by the duality.</p>

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Generalized fractional integral operators on Morrey spaces and their bi-preduals

  • 期刊论文

  • 发表日期：

    2025年7月11日

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  • Satoshi Yamaguchi,
  • Eiichi Nakai

摘要

In this paper we prove the boundedness of the generalized fractional integral operator \(I_{\rho }\) I ρ on generalized Morrey spaces with variable growth condition, which is an improvement of previous results, and then, we establish the boundedness of \(I_{\rho }\) I ρ on their bi-preduals. We also prove the boundedness of \(I_{\rho }\) I ρ on their preduals by the duality.