Compact composition operators on the Bloch space in polydiscs  

作　　者：周泽华 史济怀 

出　　处：《Science China Mathematics》2001年第3期286-291,共6页中国科学：数学（英文版）

基　　金：This work was supported in part by the National Natural Science Foundation of China ( Grant No. 19871081).

摘　　要：Let Un be the unit polydisc of ?n and φ=(φ1, ?, φ n ) a holomorphic self-map of Un. As the main result of the paper, it shows that the composition operator C is compact on the Bloch space β(Un) if and only if for every ε > 0, there exists a δ > 0, such that $$\sum\limits_{k,1 = 1}^n {\left| {\frac{{\partial \phi _l }}{{\partial z_k }}(z)} \right|} \frac{{1 - |z_k |^2 }}{{1 - |\phi _l (z)|^2 }}< \varepsilon ,$$ whenever dist(φ(z), ?U n )<δ.Let Un be the unit polydisc of Cn and =(1,…n) a holomorphicself-map of Un. As the main result of the paper, it shows that the composition operator Cφ is compact on the Bloch space β(Un) if and only if for every ε>0, there exists a δ>0, such thatwhenever dist((z),Un)<δ.

关 键 词：Bloch space POLYDISC composition operator Bergman mertic 

分 类 号：O177[理学—数学]