Weighted Composition Operators on Some Weighted Spaces in the Unit Ball

Abstract

Let $B_n$ be the unit ball of $C^n$, $H({\mathbb{B}}_n)$ the space of all holomorphic functions in $B_n$. Let $u\in H(B_n)$ and $\alpha$ be a holomorphic self-map of $B_n$. For $f\in H({\mathbb{B}}_n)$, the weigthed composition operator $u{C}_{\alpha }$ is defined by $(u{C}_{\alpha }f)(z)=u(z)f(\alpha (z)),z\in B_n\mathrm{.}$ The boundedness and compactness of the weighted composition operator on some weighted spaces on the unit ball are studied in this paper.