Compact Differences of Composition Operators on Bergman Spaces Induced by Doubling Weights

Abstract

Bounded and compact differences of two composition operators acting from the weighted Bergman space A^p_omega to the Lebesgue space L^q_nu , where 0<q<p<infty and omega belongs to the class of radial weights satisfying two-sided doubling conditions, are characterized. On the way to the proofs a new description of q-Carleson measures for A^p_omega , with p>q and , involving pseudohyperbolic discs is established. This last-mentioned result generalizes the well-known characterization of q-Carleson measures for the classical weighted Bergman space A^p_alpha with -1<alpha <infty to the setting of doubling weights. The case is also briefly discussed and an open problem concerning this case is posed.