Estimates of the Bergman kernel function on pseudoconvex domains with comparable Levi form

Abstract

Let $\Omega$ be a smoothly bounded pseudoconvex domain in $\Bbb C^n$ and let $z^0\in b\O$ be a point of finite type. We also assume that the Levi form of $b\O$ is comparable in a neighborhood of $z^0$. Then we get precise estimates of the Bergman kernel function, $\ko$, and its derivatives in a neighborhood of $z^0$.