On the $p$-Bergman kernel with respect to a functional $\hat{I}¾$

Abstract

In the present paper, we generalize the notion of the $p$-Bergman kernel and the $\hat{I}¾$-Bergman kernel to the $p$-Bergman kernel with respect to a functional $\hat{I}¾$, and establish some properties of the $p$-Bergman kernel with respect to $\hat{I}¾$. We also study the relations between the $L^p$ versions of higher order Bergman kernels and $\hat{I}¾$-Bergman kernels, and as applications we give the reproofs and generalizations of some previous results of Blocki and Zwonek about higher order Bergman kernels.

33 pages