In this paper, we study generalized Hartogs triangle of exponent <InlineEquation ID="IEq6"> <EquationSource Format="TEX">$\gamma >0$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>γ</mi> <mo>></mo> <mn>0</mn> </mrow> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq7"> <EquationSource Format="TEX">$\Omega ^{n+1}_\gamma =\{(z,w)\in \mathbb {C}^n\times \mathbb {C}: |z|^\gamma< |w| < 1\}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msubsup> <mi mathvariant="normal">Ω</mi> <mi>γ</mi> <mrow> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </msubsup> <mrow> <mo>=</mo> <mo stretchy="false">{</mo> <mrow> <mo stretchy="false">(</mo> <mi>z</mi> <mo>,</mo> <mi>w</mi> <mo stretchy="false">)</mo> </mrow> <mo>∈</mo> </mrow> <msup> <mrow> <mi mathvariant="double-struck">C</mi> </mrow> <mi>n</mi> </msup> <mo>×</mo> <msup> <mrow> <mi mathvariant="double-struck">C</mi> <mo>:</mo> <mo stretchy="false">|</mo> <mi>z</mi> <mo stretchy="false">|</mo> </mrow> <mi>γ</mi> </msup> <mrow> <mo><</mo> <mo stretchy="false">|</mo> <mi>w</mi> <mo stretchy="false">|</mo> <mo><</mo> <mn>1</mn> <mo stretchy="false">}</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>, and obtain a sharp range of p for the boundedness of the Bergman projection on the domain considered here. It generalizes the results of Edholm and McNeal [J. Geom. Anal. 27, 2658-2683 (2017)] for <InlineEquation ID="IEq8"> <EquationSource Format="TEX">$n = 1$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>n</mi> <mo>=</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation> to any dimension n.

$L^p$ Boundedness of the Bergman Projection on Generalized Hartogs Triangle in $\mathbb {C}^{n+1}$

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2026年6月27日

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Qian Fu,
Guantie Deng

摘要

In this paper, we study generalized Hartogs triangle of exponent $\gamma >0$ $γ > 0$ , $\Omega ^{n+1}_\gamma =\{(z,w)\in \mathbb {C}^n\times \mathbb {C}: |z|^\gamma< |w| < 1\}$ $Ω_{γ}^{n + 1} = {(z, w) \in C^{n} \times {C : | z |}^{γ} < | w | < 1}$ , and obtain a sharp range of p for the boundedness of the Bergman projection on the domain considered here. It generalizes the results of Edholm and McNeal [J. Geom. Anal. 27, 2658-2683 (2017)] for $n = 1$ $n = 1$ to any dimension n.

\(L^p\) Boundedness of the Bergman Projection on Generalized Hartogs Triangle in \(\mathbb {C}^{n+1}\)

摘要