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

We determine the solid hull and solid core of weighted Banach spaces $H_v^{\mathrm{\infty }}$ of analytic functions $f$ such that $v\mathrm{\mid }f\mathrm{\mid }$ 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 $H_v^{\mathrm{\infty }}$ is solid, then the monomials are an (unconditional) basis of the closure of the polynomials in $H_v^{\mathrm{\infty }}$. As a consequence $H_v^{\mathrm{\infty }}$ 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.