Weighted Composition Operators from $F(p,q,s)$ to Bloch Type Spaces on the Unit Ball

Abstract

Let $\varphi (z)=({\varphi }_1(z),...,{\varphi }_n(z))$ be a holomorphic self-map of $B$ and $\psi (z)$ a holomorphic function on $B$, where $B$ is the unit ball of ${\Bbbb C}^n$. Let $0<p,s<+\infty ,-n-1<q<+\infty ,q+s>-1$ and $\alpha \ge 0,$ this paper gives some necessary and sufficient conditions for the weighted composition operator $\wco$ induced by $\varphi$ and $\psi$ to be bounded and compact between the space $\Fs$ and $\alpha$-{\sl Bloch} space ${\beta }^{\alpha }.$

26 pages

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