Differences of weighted composition operations on the unit polydisk

Abstract

Let φ1 and φ2 be holomorphic self-maps of the unit polydisk \(\mathbb{D}^N\) , and let u1 and u2 be holomorphic functions on \(\mathbb{D}^N\) . We characterize the boundedness and compactness of the difference of weighted composition operators Wφ1, u1 and Wφ2, u2 from the weighted Bergman space \(A_{\vec \alpha }^p\) , 0 −1, j = 1,..., N, to the weighted-type space Hυ∞ of holomorphic functions on the unit polydisk \(\mathbb{D}^N\) in terms of inducing symbols φ1, φ2, u1, and u2.