Communications in Analysis and Geometry

Volume 24 (2016)

Number 4

On $p$-Bergman kernel for bounded domains in $\mathbb{C}^n$

Pages: 887 – 900

DOI: http://dx.doi.org/10.4310/CAG.2016.v24.n4.a8

Authors

Jiafu Ning (College of Mathematics and Statistics, Chongqing University, Chongqing, China)

Huiping Zhang (Department of Mathematics, Information School, Renmin University of China, Beijing, China)

Xiangyu Zhou (Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China)

Abstract

In this paper, we obtain some properties of the $p$-Bergman kernels by applying $L^p$ extension theorem. We prove that for any bounded domain in $\mathbb{C}^n$, it is pseudoconvex if and only if its $p$-Bergman kernel is an exhaustion function, for any $p \in (0, 2)$. As an application, we give a negative answer to a conjecture of Tsuji.

2010 Mathematics Subject Classification

14C30, 32A35, 32J25, 32T05, 32U10, 32W05

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Published 3 November 2016