Parametrix for the localization of the Bergman metric on strictly pseudoconvex domains

TL;DR

This paper develops a parameterized localization theorem for the Bergman metric near boundary points of strictly pseudoconvex domains and proves an approximation theorem for square integrable holomorphic functions, extending existing results.

Contribution

It introduces a parameter version of the localization theorem for the Bergman metric and establishes an approximation theorem for holomorphic functions on these domains.

Findings

Parameter version of the localization theorem for Bergman metric

Approximation theorem for square integrable holomorphic functions

Extension of Graham-Kerzman type results

Abstract

We give the parameter version of localization theorem for Bergman metric near the boundary points of strictly pseudoconvex domains. The approximation theorem for square integrable holomorphic functions on such domains in the spirit of Graham-Kerzman is proved in the hereby paper, as well.