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 

出　　处：《Science China Mathematics》2008年第4期652-659,共8页中国科学：数学（英文版）

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)

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

关 键 词：BLOCH CONSTANT BLOCH MAPPING UNIVALENT ball critical point Julia lemma locally biholomorphic MAPPING Landau CONSTANT 

分 类 号：O174.5[理学—数学]