Solid hulls of weighted Banach spaces of entire functions

Bonet, José; Taskinen, Jari

doi:10.4171/RMI/996

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Revista Matemática Iberoamericana

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Volume 34, Issue 2, 2018, pp. 593–608

DOI: 10.4171/RMI/996

Published online: 2018-05-28

Solid hulls of weighted Banach spaces of entire functions

José Bonet^[1] and Jari Taskinen^[2]

(1) Universidad Politecnia de Valencia, Spain
(2) University of Helsinki, Finland

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.

Keywords: Weighted Banach spaces of entire functions, Taylor coefficients, solid hull, solid core

Bonet José, Taskinen Jari: Solid hulls of weighted Banach spaces of entire functions. Rev. Mat. Iberoam. 34 (2018), 593-608. doi: 10.4171/RMI/996