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

In this paper we investigate a class of domains $\Omega^{n+1}_k ={(z,w)\in $\mathbb{C}$^n\times $\mathbb{C}$: |z|^k < |w| < 1}$for$k \in $\mathbb{Z}$^+$ which generalizes the Hartogs triangle. we first obtain the new explicit formulas for the Bergman kernel function on these domains and further give a range of $p$ values for which the $L^p$ boundedness of the Bergman projection holds. This range of $p$ is shown to be sharp.