The Bergman kernels of generalized Bergman-Hartogs domains

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:429

Article

Hao, Yihong¹  Wang, An² 

[1] NW Univ Xian, Dept Math, Xian 710127, Peoples R China

[2] Capital Normal Univ, Sch Math Sci, Beijing 100048, Peoples R China

关键词: Bergman kernel;    Lu Qi-Keng problem;    Hartogs domain;    Homogeneous domain;   

DOI  :  10.1016/j.jmaa.2015.04.023

来源: Elsevier

【 摘 要 】

We define the generalized Bergman-Hartogs domain, which is the Hartogs domain over the product of representative bounded homogeneous domains and compute the explicit form of the Bergman kernel function. As an application of this formula, we show that the generalized Bergman Hartogs domain is a minimal domain with the origin as center. In particular, we get the volume of this domain. In addition, we also study the Lu Qi-Keng problem of the generalized Bergman Hartogs domain. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free