Bloch constant of holomorphic mappings on the unit polydisk of C^n

作     者：WANG JianFei~(1+) LIU TaiShun~2 1 College of Mathematics and Physics Information Engineering Zhejiang Normal University Jinhua 321004,China 2 Department of Mathematics Huzhou Teachers College Huzhou 313000 China 

作者机构：College of Mathematics and Physics Information Engineering Zhejiang Normal University Jinhua China Department of Mathematics Huzhou Teachers College Huzhou China 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2008年第51卷第4期

页      面：652-659页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：This work was supported by the National Natural Science Foundation of China(Grant No.10571164) Specialized Research Fund for the Doctoral Program of Higher Education(SRFDP)(Grant No.20050358052) 

主　　题：Bloch constant Bloch mapping univalent ball critical point Julia lemma locally biholomorphic mapping Landau constant 

摘      要：In this paper,we give a definition of Bloch mappings defined in the unit polydisk Dn, which generalizes the concept of Bloch functions defined in the unit disk *** is known that Bloch theorem fails unless we have some restrictive assumption on holomorphic mappings in several complex *** shall establish the corresponding distortion theorems for subfamiliesβ（K）andβloc（K） of Bloch mappings defined in the polydisk Dn,which extend the distortion theorems of Liu and Minda to higher *** an application,we obtain lower and upper bounds of Bloch constants for various subfamilies of Bloeh mappings defined in Dn.In particular,our results reduce to the classical results of Ahlfors and Landau when n=1.