Weighted composition operators acting between weighted Bbergman spaces and weighted Banach spaces of holomorphic functions on the unit ball

Abstract

We characterize boundedness and compactness ofweighted composition operators acting between weighted Bergmanspaces $A_{v,p}$ and weighted Banach spaces $H_w^{ınfty}$ ofholomorphic functions on the open unit ball of $C^N$, $N\ge 1$.Moreover, we give a sufficient condition for such an operatoracting between weighted Bergman spaces $A_{v,p}$ and $A_{w,p}$ onthe unit ball to be bounded.