Compact Differences of Weighted Composition Operators

Abstract: Compact differences of two weighted composition operators acting from the weighted Bergman space

A_{o}^{p} m e g a

to another weighted Bergman space

A_{u}^{q}

, where

0 < p l e q < i n f t y

and

o m e g a, u

belong to the class

m a t h c a l 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_{o}^{p} m e g a

, with

o m e g a i n m a t h c a l 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_{a}^{p} l p h a

with

- 1 < a l p h a < i n f t y

to the setting of doubling weights.

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