Composition Operators from $\alpha$-Bloch Spaces into $Q_K$ Type Spaces
Received:March 12, 2008  Revised:October 06, 2008
Key Words: Composition operator   analytic function   ${\cal{B}}^\alpha$ space   $K$-Carleson measure   compact $K$-Carleson measure.  
Fund Project:the National Natural Science Foundation of China (No.\,10471039); the Grant of Higher Schools' Natural Science Basic Research of Jiangsu Province of China (Nos.\,06KJD110175; 07KJB110115).
Author NameAffiliation
YU Yan Yan School of Mathematics and Physics Science, Xuzhou Institute of Technology, Jiangsu 221008, China 
LIU Yong Min Department of Mathematics, Xuzhou Normal University, Jiangsu 221116, China 
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      Suppose $\phi$ is an analytic map of the unit disk $D$ into itself, $X$ is a Banach space of analytic functions on $D$. Define the composition operator $C_\phi$: $C_\phi f=f\circ \phi$, for all $f\in X$. In this paper, the boundedness and compactness of the composition operators from $\alpha$-Bloch spaces into $Q_K(p,q)$ and $Q_{K,0}(p,q)$ spaces are discussed, where $0<\alpha<\infty$.
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