Bloch空间上复合算子的紧性

Compactness of Composition Operators on Bloch Space

设为Bloch空间，：D→D为解析函数。本文证明：由导出的复合算子C为到中的有界线性算子；而且，当时，C为紧复合算子，其中（z）为双曲导数。

Let denote the Bloch space and be the holomorphic self-maps of the unit disk D into itself. In this note,it is proved that the composition operator C induced by is a bounded linear operator from into ,and if ,then C is compact,where (z) is the hyperbolic derivative