从双曲α-Bloch空间到双曲Q_K型空间上的复合算子

Composition Operators from Hyperbolicα-Bloch Spaces into Hyperbolic Q_K Type Spaces

若φ为单位圆盘D上的解析自映射,X为D上解析函数全体构成的Banach空间.定义X上复合算子Cφ:C_φ(f)=f(?)φ,对任意f∈X.该文研究了从双曲α-Bloch空间到双曲QK型空间上复合算子的有界性的特征.另外,还给出了从D_(p,α)到QK(p,q)空间上复合算子的有界性和紧性的特征.

Supposeφis an analytic map of the unit disk D into itself,X is a Banach space of analytic functions on D.Define the composition operator Cφ：Cφ（f） = f oφ,for all f∈X. In this paper,the boundedness of the composition operators from hyperbolicα-Bloch spaces into hyperbolic QK type spaces are discussed,where 0＆lt;α≤1.Moreover,a necessary and sufficient condition for Cφfrom weighted Dirichlet space D（p,α） to QK（p,q） to be bounded or compact is given in terms of the mapφ.