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

Abstract

In this paper, we investigate a class of domains ${\Omega }_{\gamma }^{n+1}=\{(z,w)\in {\mathbb{C}}^n\times \mathbb{C}:|z{|}^{\gamma }<|w|<1\}$ 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.

18 pages; any comments are welcome; accepted by Complex Analysis and Operator Theory