  Given a continuous, radial, rapidly decreasing weight $v$ on the complex
plane $\mathbf{C}$, we study the solid hull of its associated weighted space
$H_v^\infty(\mathbf{C})$ of all the entire functions $f$ such that $v|f|$ is
bounded. The solid hull is found for a large class of weights satisfying the
condition (B) of Lusky. Precise formulations are obtained for weights of the
form $v(r)=\exp(-ar^p), a>0, p>0$. Applications to spaces of multipliers are
included.
