SHARP ESTIMATES OF ALL HOMOGENEOUS EXPANSIONS FOR A SUBCLASS OF QUASI-CONVEX MAPPINGS OF TYPE B AND ORDER a IN SEVERAL COMPLEX VARIABLESc

In this article, first, the sharp estimates of all homogeneous expansions for a subclass of quasi-convex mappings of type B and order B on the unit ball in complex Ba- nach spaces are given. Second, the sharp estimates of all homogeneous expansions for the above generalized mappings on the unit poly...

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Bibliographic Details
Published in:数学物理学报：B辑英文版 2016, Vol.36 (6), p.1804-1818
Main Author: 刘小松 刘太顺
Format: Article
Language:English
Subjects:
估计
准凸映射
单位球
多复变量
广义映射
拟凸映射
秩序
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Summary:In this article, first, the sharp estimates of all homogeneous expansions for a subclass of quasi-convex mappings of type B and order B on the unit ball in complex Ba- nach spaces are given. Second, the sharp estimates of all homogeneous expansions for the above generalized mappings on the unit polydisk in （in are also established. In particular, the sharp estimates of all homogeneous expansions for a subclass of quasi-convex mappings （include quasi-convex mappings of type A and quasi-convex mappings of type B） in several complex variables are get accordingly. Our results state that a weak version of the Bieber- bach conjecture for quasi-convex mappings of type B and order a in several complex variables is proved, and the derived conclusions are the generalization of the classical results in one complex variable.
ISSN:0252-9602
1572-9087