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

摘要

Let $Omega$ be a smoothly bounded pseudoconvex domain in $mathbb C^n$ and let $z^0in bOmega$ be a point of finite type. We also assume that the Levi form of $bOmega$ is comparable in a neighborhood of $z^0$. Then we get precise estimates of the Bergman kernel function, $K_Omega(z,w)$, and its derivatives in a neighborhood of $z^0$.