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

2023/12/20 by Ravi Shankar Jaiswal, Jaiswal, Ravi Shankar
Mathematics · #Holomorphic and Operator Theory #Algebraic and Geometric Analysis #Analytic and geometric function theory

paper · pdf · doi:10.48550/arxiv.2312.12840

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 ℂⁿ. 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.

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