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<p>Let <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41980_2025_986_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="71" /> </InlineMediaObject> <EquationSource Format="TEX">\(L(\beta ,p,\omega )\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>L</mi> <mo stretchy="false">(</mo> <mi>β</mi> <mo>,</mo> <mi>p</mi> <mo>,</mo> <mi>ω</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41980_2025_986_Article_IEq2.gif" Format="GIF" Height="22" Rendition="HTML" Resolution="72" Type="Linedraw" Width="32" /> </InlineMediaObject> <EquationSource Format="TEX">\(\dot{\Lambda }_{\beta ,\omega }\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mover accent="true"> <mi mathvariant="normal">Λ</mi> <mo>˙</mo> </mover> <mrow> <mi>β</mi> <mo>,</mo> <mi>ω</mi> </mrow> </msub> </math></EquationSource> </InlineEquation> be weighted Lipschitz spaces of Morrey–Campanato type and pointwise version. We obtain some necessary and sufficient conditions for weighted boundedness of commutators of the Hardy–Littlewood maximal function and the sharp maximal function when symbols belong to such weighted Lipschitz spaces. Some new characterizations for weighted Lipschitz spaces are also given.</p>

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Weighted Lipschitz Spaces and Commutators of Maximal Functions

  • 期刊论文

  • 发表日期：

    2025年7月18日

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  • Pu Zhang,
  • Xiaomeng Zhu

摘要

Let \(L(\beta ,p,\omega )\) L ( β , p , ω ) and \(\dot{\Lambda }_{\beta ,\omega }\) Λ ˙ β , ω be weighted Lipschitz spaces of Morrey–Campanato type and pointwise version. We obtain some necessary and sufficient conditions for weighted boundedness of commutators of the Hardy–Littlewood maximal function and the sharp maximal function when symbols belong to such weighted Lipschitz spaces. Some new characterizations for weighted Lipschitz spaces are also given.