Solid hulls of weighted Banach spaces of entire functions

Abstract

Given a continuous, radial, rapidly decreasing weight $v$ on the complex plane, we study the solid hull of its associated weighted space $H_v^{\infty }(\mathbb{C})$ 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$(-a{r}^p),a>0,p>0$. Applications to spaces of multipliers are included.