The reduced Bergman kernel and its properties.

In this paper, we study some properties of the nth-order weighted reduced Bergman kernels for planar domains, n ≥ 1. Specifically, we look at Ramadanov type theorems, localization, and boundary behavior of the weighted reduced Bergman kernel and its higher-order counterparts. We also give a transformation formula for these kernels under biholomorphisms. [ABSTRACT FROM AUTHOR]