Geometry of pseudo-convex domains of finite type with locally diagonalizable Levi form and Bergman kernel

Abstract

In this paper, we give a precise description of the complex geometry of a pseudo-convex domain in C n near a boundary point of finite type where the Levi form is locally diagonalizable, and we use it to obtain sharp size estimates for the Bergman kernel and its derivatives. When all points of the boundary are of that type, we deduce from those estimates the L p regularity of the Bergman projection.