Abstract
Compact differences of two weighted composition operators acting from the weighted Bergman space A^p_{omega } to another weighted Bergman space A^q_{nu }, where 0<ple q<infty and omega ,nu belong to the class {mathcal {D}} of radial weights satisfying two-sided doubling conditions, are characterized. On the way to the proof a new description of q-Carleson measures for A^p_{omega }, with omega in {mathcal {D}}, in terms of 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.
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