Abstract:

Let $\mu$ be a normal function on $[0, 1)$. Suppose that $\varphi$ is a holomorphic self-map on the unit ball $B$ in ${\bf C}^{n}$ and $\psi\in H(B)$. Here the authors characterize the boundedness and compactness of the weighted composition operator $\psi C_{\varphi}$ on the Zygmund-type space ${\cal Z}_{\mu}(B)$ with a normal weight $\mu$ on the unit ball in ${\bf C}^{n}$.

Key words: Normal weight Zygmund space, High dimensions, Composition operator, Boundedness, Compactness