Transformation formula for the Reduced Bergman kernel and its Application

TL;DR

This paper establishes transformation formulas for the reduced Bergman kernel under proper holomorphic correspondences and maps, including weighted cases, and demonstrates an application of these formulas in complex analysis.

Contribution

It introduces new transformation formulas for the reduced Bergman kernel under various holomorphic mappings, extending previous results in the field.

Findings

Transformation formula for reduced Bergman kernels under proper holomorphic correspondences

Transformation formula for reduced Bergman kernels under proper holomorphic maps

Application demonstrating the utility of the transformation formula

Abstract

In this article, we prove the transformation formula for the reduced Bergman kernels under proper holomorphic correspondences between bounded domains in the complex plane. As a corollary, we obtain the transformation formula for the reduced Bergman kernels under proper holomorphic maps. We also establish the transformation formula for the weighted reduced Bergman kernels under proper holomorphic maps. Finally, we provide an application of this transformation formula.