ON SOLID CORES AND HULLS OF WEIGHTED BERGMAN SPACES [Formula omitted]

We consider weighted Bergman spaces [Formula omitted] on the unit disc as well as the corresponding spaces of entire functions, defined using non-atomic Borel measures with radial symmetry. By extending the techniques from the case of reflexive Bergman spaces, we characterize the solid core of [Formula omitted]. Also, as a consequence of a characterization of solid [Formula omitted]-spaces, we show that, in the case of entire functions, there indeed exist solid [Formula omitted]-spaces. The second part of the article is restricted to the case of the unit disc and it contains a characterization of the solid hull of [Formula omitted], when [Formula omitted] equals the weighted Lebesgue measure with the weight v. The results are based on the duality relation of the weighted [Formula omitted]- and [Formula omitted]-spaces, the validity of which requires the assumption that [Formula omitted] belongs to the class [Formula omitted], studied in a number of publications; moreover, v has to satisfy the condition (b), introduced by the authors. The exponentially decreasing weight [Formula omitted] provides an example satisfying both assumptions.