Differences of composition operators on weighted Bergman spaces

Abstract

We obtain a new boundedness criterion for the difference of two composition operators from a weighted Bergman space Aαp into a Lebesgue space Lq(μ) , where 0 < q< p and α> - 1. As a consequence, we provide a direct proof that such a bounded difference operator is necessarily compact. We also characterize compact differences of composition operators from Aαp into Aβq explicitly for 0 < p≤ q and α, β> - 1.