# Solid hulls of weighted Banach spaces of entire functions

### José Bonet

Universidad Politecnia de Valencia, Spain### Jari Taskinen

University of Helsinki, Finland

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## 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$(-ar^p), a > 0, p > 0$. Applications to spaces of multipliers are included.

## Cite this article

José Bonet, Jari Taskinen, Solid hulls of weighted Banach spaces of entire functions. Rev. Mat. Iberoam. 34 (2018), no. 2 pp. 593–608

DOI 10.4171/RMI/996