Boundary behaviour of the Bergman and Szegő kernels on generalized decoupled domains

Abstract

We prove optimal estimates of the Bergman and Szegő kernels on the diagonal, and the Bergman metric near the boundary of bounded smooth generalized decoupled pseudoconvex domains in ${\mathbb{C}}^n$. The generalized decoupled domains we consider allow the following possibilities: (a) complex tangential directions need not be decoupled separately, and (b) boundary points could have both finite and infinite type directions.

23 pages, comments welcome