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<p>We study compactness of Hankel and Toeplitz operators on Bergman spaces of convex Reinhardt domains in <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="43037_2025_445_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">\({\mathbb {C}}^2\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">C</mi> </mrow> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation> and we restrict the symbols to the class of functions that are continuous on the closure of the domain. We prove that Toeplitz operators as well as the Hermitian squares of Hankel operators are compact if and only if the Berezin transforms of the operators vanish on the boundary of the domain.</p>

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Compactness of Hankel and Toeplitz operators on convex Reinhardt domains in \({\mathbb {C}}^2\)

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年7月19日

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  • Nazlı Doğan,
  • Sönmez Şahutoğlu

摘要

We study compactness of Hankel and Toeplitz operators on Bergman spaces of convex Reinhardt domains in \({\mathbb {C}}^2\) C 2 and we restrict the symbols to the class of functions that are continuous on the closure of the domain. We prove that Toeplitz operators as well as the Hermitian squares of Hankel operators are compact if and only if the Berezin transforms of the operators vanish on the boundary of the domain.