从加权Bloch空间到Qk(p,q)空间的复合算子

假设$phi$是单位圆$D$上一个解析自映射,$X$是单位圆$D$上一个Banach空间. 定义$X$上复合算子:$C_{phi}: C_{phi}(f)=f o phi$,对所有的$fin X$. 本文利用$K-$Carleson测度刻画了$B_{log}^{alpha}(B_{log,0}^{alpha})$空间到$Q_{k}(p, q)(Q_{k, 0}(p, q))$空间的复合算子的有界性,以及$B_{log}^{alpha}(B_{log,0}^{alpha})$空间到$Q_{k,0}(p, q)$空间的复合算子的有界性和紧性.

Composition operators from weighted Bloch spaces to Qk(p,q) spaces

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 $C_{phi}: C_{phi}(f)=f o phi$, for all $fin X$. In this paper,we use K-carleson measure to discuss the bounded composition operators from $B_{log}^{alpha}(B_{log,0}^{alpha})$ to $Q_{k}(p, q)(Q_{k,0}(p, q))$ and the bounded and compact composition operators from $B_{log}^{alpha}(B_{log,0}^{alpha})$ to $Q_{k,0}(p, q)$, where $0alphainfty$.