On Decomposition Theorem of normalized biholomorphic convex mappings in Reinhardt domains  

作　　者：张文俊 刘太顺 

机构地区：[1]Department of Mathematics, Shenzhen University Normal College [2]Department of Mathematics, University of Science and Technology of China

出　　处：《Science China Mathematics》2003年第1期94-106,共13页中国科学：数学（英文版）

基　　金：This work was supported by 973 Project, the National Natural Science Foundation of China (Grant No. 19871081); the Natural Science Foundation of Guangdong Province and Anhui Province.

摘　　要：The construction of normalized biholomorphic convex mappings in the Reinhardt domain $D_p = \{ (z_1 ,z_2 , \cdots ,z_n ) \in \mathbb{C}^n :\left| {z_1 } \right|^{p_1 } + \left| {z_2 } \right|^{p_2 } + \cdots + \left| {z_n } \right|^{p_n } < 1\} $ , p j > 2, j = 1,2,?, n) of ? n is discussed. The authors set up a Decomposition Theorem for such mappings. As a special case, it is proved that, for each such mapping f, the first k-terms of the homogeneous expansion of its j-th component f j , j = 1, 2, ?, n, depends only on z j , where k is the number that satisfies k < min {p 1, p 2,?, p n ≤ k + 1. When p1,p2, ... ,pn → ∞ , this derives the Decomposition Theorem of normalized biholomorphic convex mappings in the polydisc which was gotten by T.J. Suffridge in 1970.The construction of normalized biholomorphic convex mappings in the Reinhardt domain Dp{(z1,z2,....zn):z1 p1+z1 p2+....+zn pn <1},(pj>2,j=1,2,.....n,) of n is discussed.The authors set up a Decomposition Theorem for such mappings. As a special case, it is proved that, for each suchthis derives the Decomposition Theorem of normalized biholo morphic convex mappings in the polydisc whichwas gotten by T.J. Suffridge in 1970.

关 键 词：Reinhardt domain biholomorphic convex mapping Schwarz Lemma Schwarz Lemma 

分 类 号：O177[理学—数学]