Boundary behaviour of the Bergman and Szeg\H{o} kernels on generalized decoupled domains

Abstract

We prove optimal estimates of the Bergman and Szeg\H{o} 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.