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<p>In this paper, we revisit the boundedness and compactness of the commutator of the Cauchy–Szegő projection on a bounded strictly pseudoconvex domain <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\Omega \)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">Ω</mi> </math></EquationSource> </InlineEquation> with smooth boundary <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\partial \Omega \)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>∂</mi> <mi mathvariant="normal">Ω</mi> </mrow> </math></EquationSource> </InlineEquation>, and establish the Schatten class estimate of such commutator via studying the structures of the local Besov space and establishing Taylor’s expansion on <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\partial \Omega \)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>∂</mi> <mi mathvariant="normal">Ω</mi> </mrow> </math></EquationSource> </InlineEquation>.</p>

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Local Besov spaces and commutator of the Cauchy–Szegő projection on a strictly pseodoconvex domain with smooth boundary

  • 期刊论文

  • 发表日期：

    2026年1月12日

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  • Steven G. Krantz,
  • Ji Li,
  • Chong-Wei Liang,
  • Chun-Yen Shen

摘要

In this paper, we revisit the boundedness and compactness of the commutator of the Cauchy–Szegő projection on a bounded strictly pseudoconvex domain \(\Omega \) Ω with smooth boundary \(\partial \Omega \) ∂ Ω , and establish the Schatten class estimate of such commutator via studying the structures of the local Besov space and establishing Taylor’s expansion on \(\partial \Omega \) ∂ Ω .