On the $p$-Bergman kernel with respect to a functional $\xi$

Shijie Bao, Qi’an Guan and Xun Sun

Vol. 345 (2026), No. 2, 239–277

DOI: 10.2140/pjm.2026.345.239

Abstract

We generalize the notion of the $p$-Bergman kernel and the $\xi$-Bergman kernel to the $p$-Bergman kernel with respect to a functional $\xi$, and establish some properties of the $p$-Bergman kernel with respect to $\xi$. We also study the relations between the $L^p$ versions of higher-order Bergman kernels and $\xi$-Bergman kernels. As applications we give new proofs and generalizations of some previous results of Błocki and Zwonek about higher-order Bergman kernels.

Keywords

Bergman kernel, plurisubharmonic function

Mathematical Subject Classification

Primary: 32A36

Secondary: 32A70, 32D15, 32L05, 32U05

Milestones

Received: 18 December 2025

Revised: 18 July 2026

Accepted: 19 August 2026

Published: 26 October 2026