Letφbe 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...Letφbe 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 A2γ(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.展开更多
基金supported by National Natural Science Foundation of China(Grant No.10571044)
文摘Letφbe 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 A2γ(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.
