Solid cores and solid hulls of weighted Bergman spaces

Abstract

We determine the solid hull for $2<p<\infty$ and the solid core for $1<p<2$ of weighted Bergman spaces $A_{\mu }^p,1<p<\infty$, 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 $A_{\mu }^p,1<p<\infty$, is solid if and only if the monomials are an unconditional basis of this space.