$L^p$ 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 $Ω^{n+1}_γ=\{(z,w)\in \mathbb{C}^n\times \mathbb{C}: |z|^γ< |w| < 1\}$ for $γ>0$ 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.