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<p>A general concept of a Hausdorff-type operator that absorbs all types of operators bearing the name “Hausdorff operator” and many others is considered. The characteristic features of this concept are the consideration of kernels depending on an external variable and the action between two different arbitrary sets. Generalizations and analogs of classical results on <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10958_2025_8016_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">\(L^q\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mi>q</mi> </msup> </math></EquationSource> </InlineEquation>-<InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10958_2025_8016_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">\(L^p\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mi>p</mi> </msup> </math></EquationSource> </InlineEquation> boundedness of various types of Hausdorff operators are proved for the case of such operators. Examples are considered.</p>

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\(L^q\)-\(L^p\) BOUNDEDNESS OF GENERIC HAUSDORFF-TYPE OPERATORS WITH BI-VARIABLE KERNELS

  • 期刊论文

  • 发表日期：

    2025年10月28日

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  • A. R. Mirotin

摘要

A general concept of a Hausdorff-type operator that absorbs all types of operators bearing the name “Hausdorff operator” and many others is considered. The characteristic features of this concept are the consideration of kernels depending on an external variable and the action between two different arbitrary sets. Generalizations and analogs of classical results on \(L^q\) L q - \(L^p\) L p boundedness of various types of Hausdorff operators are proved for the case of such operators. Examples are considered.