The Reduced Bergman Kernel and its Properties

TL;DR

This paper investigates the properties of higher-order weighted reduced Bergman kernels in planar domains, focusing on their boundary behavior, localization, transformation under biholomorphisms, and related theorems.

Contribution

It provides new results on Ramadanov type theorems, localization, boundary behavior, and transformation formulas for weighted reduced Bergman kernels of arbitrary order.

Findings

Established boundary behavior of the kernels

Proved localization properties

Derived transformation formulas under biholomorphisms

Abstract

In this article, we study some properties of the $n$-th order weighted reduced Bergman kernels for planar domains, $n\geq 1$. Specifically, we look at Ramadanov type theorems, localization, and boundary behaviour of the weighted reduced Bergman kernel and its higher-order counterparts. We also give a transformation formula for these kernels under biholomorphisms.