ON SOLID CORES AND HULLS OF WEIGHTED BERGMAN SPACES Aμ1

We consider weighted Bergman spaces A μ 1 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 A μ 1 . Also, as a consequence of a characterization of solid A μ 1 -spaces, we show that, in the case of entire functions, there indeed exist solid A μ 1 -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 A μ 1 , when μ equals the weighted Lebesgue measure with the weight v . The results are based on the duality relation of the weighted A 1 - and H ∞ -spaces, the validity of which requires the assumption that - log v belongs to the class W 0 , studied in a number of publications; moreover, v has to satisfy the condition ( b ), introduced by the authors. The exponentially decreasing weight v ( z ) = exp ( - 1 / ( 1 - | z | ) provides an example satisfying both assumptions.