Essential normality of linear fractional composition operators in the unit ball of C^N  

作　　者：JIANG LiangYing1,2& OUYANG CaiHeng3 1Department of Mathematics,Tongji University,Shanghai 200092,China 2Department of Applied Mathematics,Shanghai Finance University,Shanghai 201209,China 3Wuhan Institute of Physics and Mathematics,Chinese Academy of Sciences,Wuhan 430071,China 

出　　处：《Science China Mathematics》2009年第12期2668-2678,共11页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant No.10571044)

摘　　要：Let φ be a linear fractional self-map of the ball BN with a boundary fixed point e1,we show that1φReφ1(z)～Re(1-z1)holds in a neighborhood of e1 on BN.Applying this result we give a positive answer for a conjecture by MacCluer and Weir,and improve their results relating to the essential normality of composition operators on H 2(BN)and A2 γ (BN)(γ>-1).Combining this with other related results in MacCluer& Weir,Integral Equations Operator Theory,2005,we characterize the essential normality of composition operators induced by parabolic or hyperbolic linear fractional self-maps of B2.Some of them indicate a difference between one variable and several variables.Let φ be a linear fractional self-map of the ball BN with a boundary fixed point e1,we show that1φReφ1(z)～Re(1-z1)holds in a neighborhood of e1 on BN.Applying this result we give a positive answer for a conjecture by MacCluer and Weir,and improve their results relating to the essential normality of composition operators on H 2(BN)and A2 γ (BN)(γ>-1).Combining this with other related results in MacCluer& Weir,Integral Equations Operator Theory,2005,we characterize the essential normality of composition operators induced by parabolic or hyperbolic linear fractional self-maps of B2.Some of them indicate a difference between one variable and several variables.

关 键 词：composition operators essential NORMALITY HARDY space BERGMAN SPACES 

分 类 号：O177[理学—数学]