Weighted Composition Operators from Banach Spaces of Holomorphic Functions to Weighted-Type Banach Spaces on the Unit Ball in Cn.

Let X be a Banach space of holomorphic functions on the unit ball B n in C n whose point-evaluation functionals are bounded. In this work, we characterize the bounded weighted composition operators from X into a weighted-type Banach space H μ ∞ (B n) , where the weight μ is an arbitrary positive continuous function on B n . We determine the norm of such operators in terms of the norm of the point-evaluation functionals. Under some restrictions on X, we characterize the compact weighted composition operators mapping X into H μ ∞ (B n) . Under an alternative set of conditions, we provide essential norm estimates. We apply our results to the cases when X is the Hardy space H p (B n) , the weighted Bergman space A α p (B n) for α > - 1 and 1 ≤ p < ∞ , the Bloch space B and the little Bloch space B 0 . In all these cases we obtain precise formulas of the essential norm. [ABSTRACT FROM AUTHOR]