On \(p\)-Bergman kernel for bounded domains in \(\mathbb{C}^n\)
type: Item
instance of: scholarly article
title: On \(p\)-Bergman kernel for bounded domains in \(\mathbb{C}^n\)
zbMATH Open document ID: 1368.32004
published in: Communications in Analysis and Geometry
publication date: 2017-01-12T00:00:00Z
review text: The \(p\)-Bergman kernel in bounded open subsets of \(\mathbb C ^n\) is studied. Its definition is obtained from the one of the usual Bergman kernel (for \(p=2\)) by replacing the exponent \(2\) with \(p\). The authors prove some of the properties applying the \(L^p\) generalization of the Ohsawa-Takegoshi extension theorem. In particular they show that a bounded domain in \(\mathbb C ^n\) is pseudoconvex iff its \(p\)-Bergman kernel is an exhaustion function for all \(p\in (0,2)\). They also disprove a conjecture of H. Tsuji concerning the asymptotic behaviour of the Bergman kernels related to sections of \(m\) multiples of the canonical bundle of the punctured disc.
Mathematics Subject Classification ID: 32A25
Mathematics Subject Classification ID: 32A35
Mathematics Subject Classification ID: 32T05
Mathematics Subject Classification ID: 32U10
zbMATH DE Number: 6674138
zbMATH Keywords: Bergman kernel
zbMATH Keywords: pseudoconvex domains
author: Jiafu Ning
author: Huiping Zhang
author: Xiangyu Zhou
reviewed by: Slawomir Kołodziej
MaRDI profile type: Publication
full work available at URL: cag.2016.v24.n4.a8
OpenAlex ID: W2546970426
DOI: 10.4310/CAG.2016.V24.N4.A8
description: scientific article; zbMATH DE number 6674138