$L^p$ 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 $\Omega^{n+1}_\gamma ={(z,w)\in \mathbb{C}^n\times \mathbb{C}: |z|^\gamma < |w| < 1}$ 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.