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<p>Monomial polyhedra are a class of bounded singular Reinhardt domains defined as sublevel sets of holomorphic monomials, which include the well-known Hartogs triangle and its various generalizations as examples. In this paper, we give complete characterizations for <InlineEquation ID="IEq1"> <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 monomial polyhedra. As applications of our main results, we investigate the boundedness and compactness of composition operators and Toeplitz operators on such domains.</p>

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Carleson measures on a class of singular Reinhardt domains and their applications

  • 期刊论文

  • 发表日期：

    2025年11月8日

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  • Yanyan Tang,
  • Shuo Zhang

摘要

Monomial polyhedra are a class of bounded singular Reinhardt domains defined as sublevel sets of holomorphic monomials, which include the well-known Hartogs triangle and its various generalizations as examples. In this paper, we give complete characterizations for \((p,q;\alpha )\) ( p , q ; α ) -Carleson and vanishing Carleson measures on monomial polyhedra. As applications of our main results, we investigate the boundedness and compactness of composition operators and Toeplitz operators on such domains.