Weighted Composition Operators between Bergman Spaces with Exponential Weights.

In this paper, we study some properties of weighted composition operators on a class of weighted Bergman spaces A φ p with 0 < p ≤ ∞ and φ ∈ W 0 . Also, we completely characterize the q-Carleson measure for A φ p in terms of the averaging function and the generalized Berezin transform with 0 < q < ∞. As applications, the boundedness and compactness of weighted composition operators acting from one Bergman space A φ p to another A φ q are equivalently described and the Schatten class property of the weighted composition operator acting on A φ 2 are given. Our main results are expressed in terms of certain Berezin type integral transforms. [ABSTRACT FROM AUTHOR]