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<p>In this article, we consider a certain domain <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11785_2025_1845_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="36" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathscr {D}_{p,m}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="script">D</mi> <mrow> <mi>p</mi> <mo>,</mo> <mi>m</mi> </mrow> </msub> </math></EquationSource> </InlineEquation> defined by the intersection of cylindrical Fock-Bargmann-Hartogs domains. We obtain an explicit form of the Bergman kernel of <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11785_2025_1845_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="36" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathscr {D}_{p,m}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="script">D</mi> <mrow> <mi>p</mi> <mo>,</mo> <mi>m</mi> </mrow> </msub> </math></EquationSource> </InlineEquation>. As an application, we prove that <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11785_2025_1845_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="36" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathscr {D}_{p,m}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="script">D</mi> <mrow> <mi>p</mi> <mo>,</mo> <mi>m</mi> </mrow> </msub> </math></EquationSource> </InlineEquation> is a Lu Qi-Keng domain for any <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11785_2025_1845_Article_IEq4.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="54" /> </InlineMediaObject> <EquationSource Format="TEX">\(p \in \mathbb R_{+}^m\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>p</mi> <mo>∈</mo> <msubsup> <mi mathvariant="double-struck">R</mi> <mrow> <mo>+</mo> </mrow> <mi>m</mi> </msubsup> </mrow> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11785_2025_1845_Article_IEq5.gif" Format="GIF" Height="15" Rendition="HTML" Resolution="72" Type="Linedraw" Width="47" /> </InlineMediaObject> <EquationSource Format="TEX">\(m \ge 2\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>m</mi> <mo>≥</mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation>.</p>

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The Bergman Kernel for the Intersection of Cylindrical Fock-Bargmann-Hartogs Domains

  • 期刊论文

  • 发表日期：

    2025年11月7日

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  • Atsushi Yamamori

摘要

In this article, we consider a certain domain \(\mathscr {D}_{p,m}\) D p , m defined by the intersection of cylindrical Fock-Bargmann-Hartogs domains. We obtain an explicit form of the Bergman kernel of \(\mathscr {D}_{p,m}\) D p , m . As an application, we prove that \(\mathscr {D}_{p,m}\) D p , m is a Lu Qi-Keng domain for any \(p \in \mathbb R_{+}^m\) p ∈ R + m and \(m \ge 2\) m ≥ 2 .