Boundary behavior of the Bergman kernel function on some pseudoconvex domains in ${\bf C}\sp n$

Abstract

Let Q be a bounded pseudoconvex domain in Cn with smooth defining function r and let zo E bfQ be a point of finite type. We also assume that the Levi form Thr(z) of bQ2 has (n 2)-positive eigenvalues at zo. Then we get a quantity which bounds from above and below the Bergman kernel function in a small constant and large constant sense.