Revista Matemática Iberoamericana
Full-Text PDF (253 KB) | Metadata | Table of Contents | RMI summary
Published online: 2018-05-28
Solid hulls of weighted Banach spaces of entire functionsJosé Bonet and Jari Taskinen (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