从$\alpha$-Bloch空间到$Q_K$型空间的复合算子

Composition Operators from $\alpha$-Bloch Spaces into $Q_K$ Type Spaces

中文关键词:  复合算子  解析函数  ${\cal{B}}^\alpha$ 空间  $K$-Carleson 测度  紧 $K$-Carleson 测度.

英文关键词:Composition operator  analytic function  ${\cal{B}}^\alpha$ space  $K$-Carleson measure  compact $K$-Carleson measure.

中文摘要:

      若 $\phi$ 为单位圆盘 $D$ 上解析自映射, $X$为$D$上解析函数全体构成的Banach空间. 定义 $X$上复合算子$C_\phi$ ：$C_\phi (f)=f\circ \phi$, 对任意 $f\in X$.本文给出了从 ${\cal{B}}^\alpha$到$Q_K(p,q)$ 及 $Q_{K,0}(p,q)$ 空间上复合算子的有界性和紧性的特征.

英文摘要:

      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 $0<\alpha<\infty$.