一类有界Reinhardt域上的函数论

数学季刊 ›› 2006, Vol. 21 ›› Issue (1): 115-123.

一类有界Reinhardt域上的函数论

Function Theory of a Class of Bounded Reinhardt DomainsLI Xian (University, Kaifeng 475001, China

收稿日期:2004-12-31 出版日期:2006-03-30 发布日期:2023-12-25
作者简介:LI Xian(1967-),female,native of Nanyang,Henan,a lecturer of Henan University,M.S.D., engages in several comples variables.
基金资助:
Supported by the NSF of Henan University(04YBRW043)

Function Theory of a Class of Bounded Reinhardt Domains

Function Theory of a Class of Bounded Reinhardt DomainsLI Xian (University, Kaifeng 475001, China

Received:2004-12-31 Online:2006-03-30 Published:2023-12-25
About author:LI Xian(1967-),female,native of Nanyang,Henan,a lecturer of Henan University,M.S.D., engages in several comples variables.
Supported by:
Supported by the NSF of Henan University(04YBRW043)

摘要/Abstract

摘要： In this paper, we consider a class of bounded Reinhardt domains D_α(m, n₁,…,n_m). The Bergman kernel function K(z,z), the Bergman metric matrix T(z,z), the Cauchy-Szego kernel function S(z,ζ) are obtained. Then we prove that the formal Poisson kernel function is not a Poisson kernel function. At last, we prove that D_αis a quasiconvex domain and D_αis a stronger quasiconvex domain if and only if D_α is a hypersphere.

关键词: bounded Reinhardt , domain;Cauchy-Szego , kernel

Abstract: In this paper, we consider a class of bounded Reinhardt domains D_α(m, n₁,…,n_m). The Bergman kernel function K(z,z), the Bergman metric matrix T(z,z), the Cauchy-Szego kernel function S(z,ζ) are obtained. Then we prove that the formal Poisson kernel function is not a Poisson kernel function. At last, we prove that D_αis a quasiconvex domain and D_αis a stronger quasiconvex domain if and only if D_α is a hypersphere.

Key words: bounded Reinhardt , domain;Cauchy-Szego , kernel

中图分类号:

O174.5

李娴. 一类有界Reinhardt域上的函数论[J]. 数学季刊, 2006, 21(1): 115-123.

LI Xian. Function Theory of a Class of Bounded Reinhardt Domains[J]. Chinese Quarterly Journal of Mathematics, 2006, 21(1): 115-123.

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