A NOTE ON SCHWARZ LEMMA FOR THE MODULUS OF HOLOMORPHIC MAPPINGS ON D  

作　　者：刘洋 戴绍虞 

机构地区：[1]Department of Mathematics, Zhejiang Normal University [2]Department of Mathematics,Jinling Institute of Technology

出　　处：《Acta Mathematica Scientia》2015年第1期89-94,共6页数学物理学报（B辑英文版）

基　　金：supported by National Natural Science Foundations of China(11011373,11201199,11271333);Zhejiang Provincial Natural Science Foundation of China(LY14A010008)

摘　　要：In this note, we consider a holomorphic mapping f from the unit disk C in C to p-ball B^p = {z∈C^n;i=1∑n｜zi｜p〈1,1〈p〈＋∞. It is proved that for such f,｜ ｜ ｜f｜｜（z）｜≤1-｜｜f（z）｜｜^2/1-｜z｜^2,z∈D. The extremal problem is also discussed when p is an even number. This result extends some related results on Schwarz lemma.In this note, we consider a holomorphic mapping f from the unit disk C in C to p-ball B^p = {z∈C^n;i=1∑n｜zi｜p〈1,1〈p〈＋∞. It is proved that for such f,｜ ｜ ｜f｜｜（z）｜≤1-｜｜f（z）｜｜^2/1-｜z｜^2,z∈D. The extremal problem is also discussed when p is an even number. This result extends some related results on Schwarz lemma.

关 键 词：Schwarz lemma holomorphic mapping p-ball 

分 类 号：O174.52[理学—数学]