Solid cores and solid hulls of weighted Bergman spaces

Abstract

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