从$A^{p}_{\alpha}$到$A^{\infty}(\varphi)$的加权复合算子

设$u \in H(D), \ \phi$为$D$上的解析自映射,定义$H(D)$上的加权复合算子为$u C_{\phi}(f)=$$uf\circ\phi$, \ $f\in H(D)$.本文得到了从$A^{p}_{\alpha}$到$A^{\infty}(\varphi)\ (A_{0}^{\infty}(\varphi))$的加权复合算子$u C_{\phi}$的有界性和紧性的充要条件.

Weighted Composition Operators from $A^{p}_{\alpha}$ to $A^{\infty}(\varphi)$

Suppose $u\in H (D)$ and $\phi$ is an analytic map of the unit disk $D$ into itself. Define the weighted composition operator $uC_\phi: uC_\phi (f)= u f\circ \phi$, for all $f\in H(D)$. In this paper, we get necessary and sufficient conditions for the bounded and compact weighted composition operators from the weighted Bergman spaces $A_{\alpha}^{p}$ to $A^{\infty}(\varphi) \ (A_{0}^{\infty}(\varphi))$ spaces.