GENERALISED WEIGHTED COMPOSITION OPERATORS ON BERGMAN SPACES INDUCED BY DOUBLING WEIGHTS.

We characterise bounded and compact generalised weighted composition operators acting from the weighted Bergman space Apω, where 0 and ω belongs to the class D of radial weights satisfying a two-sided doubling condition, to a Lebesgue space Lqν. On the way, we establish a new embedding theorem on weighted Bergman spaces Apω which generalises the well-known characterisation of the boundedness of the differentiation operator Dnn(ƒ) = ƒ(n) from the classical weighted Bergman space Apα to the Lebesgue space Lqμ, induced by a positive Borel measure μ, to the setting of doubling weights. [ABSTRACT FROM AUTHOR]