COMPOSITION OPERATORS ON THE LITTLE

COMPOSITION OPERATORS ON THE LITTLE BLOCH SPACE IN POLYDISCS

Let Un be the unit polydisc of Cn and φ = (φ1,…,φn) a holomorphic self map of Un. This paper shows that the composition operator Cφ induced by φ is bounded on the little Bloch space β0*(Un) if and only if φ∈β0*(Un) for every l=1,2,…,n, and also gives a sufficient and necessary condition for the composition operator Cφ to be compact on the little Bloch spaceβ0* (Un).

作 者： Zhou Zehua Zhu Min Shi Jihuai   作者单位： Zhou Zehua,Zhu Min(Department of Mathematics, Tianjin University, Tianjin 300072, China)

Shi Jihuai(Department of Mathematics, University of Science and Technology of China, Hefei 230026, China) 

刊 名： 数学物理学报（英文版）  ISTIC SCI 英文刊名： ACTA MATHEMATICA SCIENTIA  年，卷(期)： 2005 25(4)  分类号： O4  关键词： Little Bloch space   distinguished boundary   composition operator   Bergmanmetric  

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