Distortion theorems on the Lie ball R_(IV)(n) in C^n  

作　　者：WANG JianFei1,LIU TaiShun2 &XU HuiMing1 1College of Mathematics,Physics and Information Engineering,Zhejiang Normal University,Jinhua 321004, China 2D epartment of Mathematics,Huzhou Teachers College,Huzhou 313000,China 

出　　处：《Science China Mathematics》2009年第12期2743-2750,共8页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant No.10826083,10771064);Specialized Research Fund for the Doctoral Program of Higher Education(SRFDP)(Grant No.20050358052);Natural Science Foundation of Zhejiang Province(Grant No.D7080080,Y6090694)

摘　　要：In this paper,we introduce the subfamilies Hm(RIV(n))of holomorphic mappings defined on the Lie ball RIV(n)which reduce to the family of holomorphic mappings and the family of locally biholomorphic mappings when m=1 and m→+∞,respectively.Various distortion theorems for holomophic mappings Hm(RIV(n))are established.The distortion theorems coincide with Liu and Minda’s as the special case of the unit disk.When m=1 and m→+∞,the distortion theorems reduce to the results obtained by Gong for RIV(n),respectively.Moreover,our method is different.As an application,the bounds for Bloch constants of Hm(RIV(n))are given.In this paper,we introduce the subfamilies Hm(RIV(n))of holomorphic mappings defined on the Lie ball RIV(n)which reduce to the family of holomorphic mappings and the family of locally biholomorphic mappings when m=1 and m→+∞,respectively.Various distortion theorems for holomophic mappings Hm(RIV(n))are established.The distortion theorems coincide with Liu and Minda’s as the special case of the unit disk.When m=1 and m→+∞,the distortion theorems reduce to the results obtained by Gong for RIV(n),respectively.Moreover,our method is different.As an application,the bounds for Bloch constants of Hm(RIV(n))are given.

关 键 词：HOLOMORPHIC MAPPING distortion THEOREM BLOCH constant BLOCH MAPPING 

分 类 号：O174.52[理学—数学]