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arXiv · 2204.08715

$L^p$ boundedness of the Bergman Projection on generalizations of the Hartogs triangle in $\mathbb{C}^{n+1}$

Qian Fu·Guantie Deng
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Abstract

In this paper, we investigate a class of domains $\Omega^{n+1}_\gamma =\{(z,w)\in \mathbb{C}^n\times \mathbb{C}: |z|^\gamma < |w| < 1\}$ for $\gamma>0$ that generalizes the Hartogs triangle. We obtain a sharp range of $p$ for the boundedness of the Bergman projection on the domain considered here. It generalizes the results by Edholm and McNeal \cite{LD1} for n = 1 to any dimension n.

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Qian Fu, Guantie Deng. 2022-04-19. $L^p$ boundedness of the Bergman Projection on generalizations of the Hartogs triangle in $\mathbb{C}^{n+1}$. https://arxiv.org/abs/2204.08715

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