Solid hulls and cores of weighted $H^{\infty }$-spaces

Abstract

We determine the solid hull and solid core of weighted Banach spaces $H_v^{\infty }$ of analytic functions $f$ such that $v|f|$ is bounded, both in the case of the holomorphic functions on the disc and on the whole complex plane, for a very general class of radial weights $v$. Precise results are presented for concrete weights on the disc that could not be treated before. It is also shown that if $H_v^{\infty }$ is solid, then the monomials are an (unconditional) basis of the closure of the polynomials in $H_v^{\infty }$. As a consequence $H_v^{\infty }$ does not coincide with its solid hull and core in the case of the disc. An example shows that this does not hold for weighted spaces of entire functions.

19 pages