The Reduced Bergman Kernel and its Properties

In this article, we study some properties of the $n$-th order weighted reduced Bergman kernels for planar domains, $n\ge 1$. 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.