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<p>In this paper, we introduce a kind of weighted Fock space <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(F^p_\varphi \)</EquationSource> <EquationSource Format="MATHML"><math> <msubsup> <mi>F</mi> <mi>φ</mi> <mi>p</mi> </msubsup> </math></EquationSource> </InlineEquation> on the complex plane <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\mathbb {C}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="double-struck">C</mi> </math></EquationSource> </InlineEquation>, and obtain some estimates on the Bergman kernel function. As an application, we discuss the Bergman projection, density, and <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(L^p_\varphi \)</EquationSource> <EquationSource Format="MATHML"><math> <msubsup> <mi>L</mi> <mi>φ</mi> <mi>p</mi> </msubsup> </math></EquationSource> </InlineEquation>-regularity of the canonical solution to <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\overline{\partial }\)</EquationSource> <EquationSource Format="MATHML"><math> <mover> <mi>∂</mi> <mo>¯</mo> </mover> </math></EquationSource> </InlineEquation>.</p>

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Reproducing kernel functions in weighted Fock spaces

  • 期刊论文

  • 发表日期：

    2026年7月27日

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  • Zhangjian Hu,
  • Xiaofen Lv,
  • Alexander P. Schuster

摘要

In this paper, we introduce a kind of weighted Fock space \(F^p_\varphi \) F φ p on the complex plane \(\mathbb {C}\) C , and obtain some estimates on the Bergman kernel function. As an application, we discuss the Bergman projection, density, and \(L^p_\varphi \) L φ p -regularity of the canonical solution to \(\overline{\partial }\) ∂ ¯ .