Solid cores and solid hulls of weighted Bergman spaces

Abstract

We determine the solid hull for 2<p<∞ and the solid core for 1<p<2 of weighted Bergman spaces Aμp,1<p<∞, of analytic functions on the disk and on the whole complex plane, for a very general class of nonatomic positive bounded Borel measures μ. New examples are presented. Moreover, we show that the space Aμp,1<p<∞, is solid if and only if the monomials are an unconditional basis of this space.