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<p>The goal of this paper is to introduce tiling Morrey spaces and their weighted counterparts. A condition under which weights ensure the boundedness of important operators is established. Weights similar to the Muckenhoupt class <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10476_2025_94_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="22" /> </InlineMediaObject> <EquationSource Format="TEX">\(A_p\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>A</mi> <mi>p</mi> </msub> </math></EquationSource> </InlineEquation> within Morrey spaces are dealt with. Additionally, a full characterization of the weights for which two-weight norm inequalities for linear positive operators hold in these spaces is given. Then new class dealt with in this paper contains the one introduced recently by Lerner.</p>

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Tiling Morrey spaces – as a dyadic toy model

  • 期刊论文

  • 发表日期：

    2025年6月12日

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  • Y. Sawano,
  • H. Tanaka

摘要

The goal of this paper is to introduce tiling Morrey spaces and their weighted counterparts. A condition under which weights ensure the boundedness of important operators is established. Weights similar to the Muckenhoupt class \(A_p\) A p within Morrey spaces are dealt with. Additionally, a full characterization of the weights for which two-weight norm inequalities for linear positive operators hold in these spaces is given. Then new class dealt with in this paper contains the one introduced recently by Lerner.