DISTORTION THEOREMS FOR BLOCH MAPPINGS ON THE UNIT POLYDISC Dn

In this article, we establish distortion theorems for some various subfamilies of Bloch mappings defined in the unit polydisc Dn with critical points, which extend the results of Liu and Minda to higher dimensions. We obtain lower bounds of ｜ det（f＇（z））｜and Rdet（f＇（z）） for Bloch mapping f. As an app...

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Bibliographic Details
Published inActa mathematica scientia Vol. 30; no. 5; pp. 1661 - 1668
Main Author 王建飞 刘太顺 唐笑敏
Format Journal Article
LanguageEnglish
Published College of Mathematics Physics and Information Engineering,Zhejiang Normal University,Jinhua 321004,China%Department of Mathematics,Huzhou Teachers College,Huzhou 313000,China 01.09.2010
Subjects
Bloch常数
上下界
偏差定理
全纯映射
多圆柱
密度泛函
Bloch mapping
critical point
Bloch constant
holomorphic mapping
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Summary:In this article, we establish distortion theorems for some various subfamilies of Bloch mappings defined in the unit polydisc Dn with critical points, which extend the results of Liu and Minda to higher dimensions. We obtain lower bounds of ｜ det（f＇（z））｜and Rdet（f＇（z）） for Bloch mapping f. As an application, some lower and upper bounds of Bloch constants for the subfamilies of holomorphic mappings are given.
Bibliography:Bloch mapping
critical point
Bloch constant
O174.55
Bloch constant; Bloch mapping; critical point; holomorphic mapping
O174.56
42-1227/O
holomorphic mapping
ISSN:0252-9602
1572-9087
DOI:10.1016/S0252-9602(10)60159-2