Compactness of the differences of weighted composition operators from weighted Bergman spaces to weighted-type spaces on the unit ball

Abstract

Let Φ1 and Φ2 be holomorphic self-maps of the open unit ball B in CN, u1 and u2 be holomorphic functions on B and let weighted composition operators W Φ1,u1; WΦ2,u2: Apα → H∞v be bounded. This paper characterizes the compactness of the difference of these operators from the weighted Bergman space Apα, 0 < p < ∞, α >-1, to the weighted-type space H∞v of holomorphic functions on B in terms of inducing symbols Φ1, Φ2, u1 and u2. For the case p > 1 we find an asymptotically equivalent expression to the essential norm of the operator.