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

TL;DR

This paper determines the exact range of p for which the Bergman projection is bounded on a family of domains generalizing the Hartogs triangle in complex n+1 dimensions, extending previous results.

Contribution

It provides a sharp characterization of p for Bergman projection boundedness on generalized Hartogs triangle domains in higher dimensions.

Findings

Established the precise p-range for boundedness of the Bergman projection.

Extended previous one-dimensional results to higher dimensions.

Generalized the class of domains for Bergman projection analysis.

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.