多复变数某些双全纯映射子族精确的系数估计  

The Sharp Coefficient Estimates for Some Subclasses of Biholomorphic Mappings in Several Complex Variables

作　　者：刘小松 LIU Xiaosong(School of Mathematics and Statistics,Lingnan Normal University,Zhanjiang 524048,Guangdong,China)

机构地区：[1]岭南师范学院数学与统计学院,广东湛江524048

出　　处：《数学年刊（A辑）》2021年第1期23-32,共10页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No.11871257)的资助。

摘　　要：作者建立了复Banach空间单位球上和C^(n)中单位多圆柱上限制条件下双全纯映射齐次展开式的精确估计和Fekete-Szegö不等式,同时给出C^(n)中D_(p1,p2,…,pn)={z∈C^(n):∑ni=1|zl|^(pl)<1}(pl>1,l=1,2,…,n)上限制条件下双全纯映射主要系数的精确估计和Fekete-Szegö不等式.所得结果推广了单复变几何函数论中相应的经典结论.In this paper,the sharp estimates of all homogeneous expansions and the FeketeSzego inequality for biholomorphic mappings defined on the unit ball of complex Banach spaces and the unit polydisk in C^(n)are established with some restricted condition.Meanwhile,the sharp main coefficient estimates and the Fekete-Szegöinequality for biholomorphic mappings on D_(p1,p2,…,pn)={z∈C^(n):∑nl=1|zl|^(pl)<1}(pl>1,l=1,2,…,n)in C^(n)are given under certain additional assumption.The results generalize the corresponding classical results in one dimension of complex function theory.

关 键 词：双全纯映射 齐次展开式 主要系数估计 Fekete-Szegö不等式 

分 类 号：O174.56[理学—数学]