Ning, Jiafu; Zhang, Huiping; Zhou, Xiangyu On \(p\)-Bergman kernel for bounded domains in \(\mathbb{C}^n\). (English) Zbl 1368.32004 Commun. Anal. Geom. 24, No. 4, 887-900 (2016). 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. Reviewer: Slawomir Kołodziej (Kraków) Cited in 7 Documents MSC: 32A25 Integral representations; canonical kernels (Szegő, Bergman, etc.) 32A35 \(H^p\)-spaces, Nevanlinna spaces of functions in several complex variables 32T05 Domains of holomorphy 32U10 Plurisubharmonic exhaustion functions Keywords:Bergman kernel; pseudoconvex domains PDFBibTeX XMLCite \textit{J. Ning} et al., Commun. Anal. Geom. 24, No. 4, 887--900 (2016; Zbl 1368.32004) Full Text: DOI