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<p>In this article, the author establishes a wavelet characterization of inhomogeneous Lipschitz space <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12220_2025_2192_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="53" /> </InlineMediaObject> <EquationSource Format="TEX">\(\textrm{lip}_{\theta }(\mathcal {X})\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mtext>lip</mtext> <mi>θ</mi> </msub> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="script">X</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> via Carleson sequence, where <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12220_2025_2192_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathcal {X}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="script">X</mi> </math></EquationSource> </InlineEquation> is a space of homogeneous type introduced by R. R. Coifman and G. Weiss. As applications, characterizations of several geometric conditions on <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12220_2025_2192_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathcal {X}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="script">X</mi> </math></EquationSource> </InlineEquation>, involving the upper bound, the lower bound, and the Ahlfors regular condition, are obtained.</p>

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Wavelet Characterization of Inhomogeneous Lipschitz Spaces on Spaces of Homogeneous Type and Its Applications

  • 期刊论文

  • 发表日期：

    2025年9月15日

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  • Fan Wang

摘要

In this article, the author establishes a wavelet characterization of inhomogeneous Lipschitz space \(\textrm{lip}_{\theta }(\mathcal {X})\) lip θ ( X ) via Carleson sequence, where \(\mathcal {X}\) X is a space of homogeneous type introduced by R. R. Coifman and G. Weiss. As applications, characterizations of several geometric conditions on \(\mathcal {X}\) X , involving the upper bound, the lower bound, and the Ahlfors regular condition, are obtained.