Solid hulls of weighted Banach spaces of entire functions

Given a continuous, radial, rapidly decreasing weight $v$ on the complex plane $\mathbf{C}$, we study the solid hull of its associated weighted space $H_v^{\mathrm{\infty }}(\mathbf{C})$ of all the entire functions $f$ such that $v\mathrm{\mid }f\mathrm{\mid }$ 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 $v(r)=\exp (-a{r}^p),a>0,p>0$. Applications to spaces of multipliers are included.