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<p>In this paper, we characterize the <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12220_2025_2114_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="56" /> </InlineMediaObject> <EquationSource Format="TEX">\((p,q;\alpha )\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>p</mi> <mo>,</mo> <mi>q</mi> <mo>;</mo> <mi>α</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>-Carleson and vanishing Carleson measures on bounded <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12220_2025_2114_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathbb {C}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="double-struck">C</mi> </math></EquationSource> </InlineEquation>-convex domains whose Bergman kernel is of sharp <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12220_2025_2114_Article_IEq3.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="16" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathcal {B}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="script">B</mi> </math></EquationSource> </InlineEquation>-type. This class of domains includes convex domains of finite type and some other weakly pseudoconvex domains. As applications of our main results, we study the boundedness and compactness of composition and Toeplitz operators on Bergman spaces over such domains.</p>

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Carleson Measures on Weakly Pseudoconvex Domains

  • 期刊论文

  • 发表日期：

    2025年7月17日

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  • Shuo Zhang

摘要

In this paper, we characterize the \((p,q;\alpha )\) ( p , q ; α ) -Carleson and vanishing Carleson measures on bounded \(\mathbb {C}\) C -convex domains whose Bergman kernel is of sharp \(\mathcal {B}\) B -type. This class of domains includes convex domains of finite type and some other weakly pseudoconvex domains. As applications of our main results, we study the boundedness and compactness of composition and Toeplitz operators on Bergman spaces over such domains.