Composition operators on the little Bloch space in polydiscs

被引：0
|
作者：
Zhou, ZH [1 ]
Zhu, M
Shi, JH
机构：
[1] Tianjin Univ, Dept Math, Tianjin 300072, Peoples R China
[2] Univ Sci & Technol China, Dept Math, Hefei 230026, Peoples R China
来源：
ACTA MATHEMATICA SCIENTIA | 2005年 / 25卷 / 04期
关键词：
little Bloch space; distinguished boundary; composition operator; Bergman metric;
D O I：
10.1016/S0252-9602(17)30202-3
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let U-n be the unit polydisc of C-n and phi = (phi(1),..., phi(n)) a holomorphic self-map of U-n. This paper shows that the composition operator C-phi induced by 0 is bounded on the little Bloch space beta(o*) (U-n) if and only if phi(1) is an element of beta(0*) (U-n) for every l = 1,2,..., n, and also gives a sufficient and necessary condition for the composition operator C-phi to be compact on the little Bloch space beta(0*) (U-n).
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页码：629 / 638
页数：10
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