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

Abstract

We determine the solid hull and solid core of weighted Banach spaces $$H_v^\infty $$ of analytic functions 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.