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 Name Affiliation 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 $0<\alpha<\infty$.