Weighted Composition Operators between different Bloch-type Spaces in Polydisk

Abstract

Let $ϕ(z)=(ϕ_1(z), ...,ϕ_n(z))$ be a holomorphic self-map of $U^n$ and $ψ(z)$ a holomorphic function on $U^n,$ where $U^n$ is the unit polydisk of ${\Bbb C}^n.$ Let $p\geq 0,$ $q\geq 0$, this paper gives some necessary and sufficient conditions for the weighted composition operator $W_{ψ,ϕ}$ induced by $ψ$ and $ϕ$ to be bounded and compact between $p$-Bloch space ${\cal B}^p(U^n)$ and $q$-Bloch space ${\cal B}^q(U^n).$