Boundary behavior of the Bergman kernel for generalized Fock-Bargmann-Hartogs domains

被引：0

作者：

Park, Jong-Do ^{[1
,2
]}

机构：

[1] Kyung Hee Univ, Dept Math, Seoul 02447, South Korea

[2] Kyung Hee Univ, Res Inst Basic Sci, Seoul 02447, South Korea

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2022年 / 509卷 / 01期

基金：

新加坡国家研究基金会;

关键词：

Bergman kernel; Generalized Fock space  Mittag-Leffler function; Boundary behavior; Generalized Fock-Bargmann-Hartogs domains; BIHOLOMORPHIC-MAPPINGS; FORMULAS;

D O I：

10.1016/j.jmaa.2021.125909

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study the Bergman kernel for the Hartogs type domain D-mu,D-p := (z, zeta) is an element of C x C-n : II zeta II2 < e(-mu|z|p)}. In particular, we compute the explicit form of the Bergman kernel for D-mu,D-2/m for any positive integer m. The relations between the Mittag-Leffler function and the generalized Fock kernel are investigated. Using the explicit formula, we study the asymptotic behavior of the Fock kernel and the boundary behavior of the Bergman kernel on the diagonal for the generalized Fock-Bargmann-Hartogs domains D-mu,D-2/m. (c) 2021 Elsevier Inc. All rights reserved.

引用

页数：14

共 23 条

[21] The Asymptotic Behavior of the Bergman Kernel on Pseudoconvex Model Domains
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[22] Behavior of the Bergman kernel and metric near convex boundary points
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PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2003, 131 (07) : 2097 - 2102
[23] Behavior of the Bergman kernel near smooth convex boundary points
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