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# 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

#### 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