A note on completeness of weighted Banach spaces of analytic functions

José Bonet, Dragan Vukotić

Published 2016-07-28Version 1

Given a non-negative weight $v$, not necessarily bounded or strictly positive, defined on a domain $G$ in the complex plane, we consider the weighted space $H_v^\infty(G)$ of all holomorphic functions on $G$ such that the product $v|f|$ is bounded in $G$ and study the question of when is such a space complete. We obtain both some necessary and some sufficient conditions, exhibit several relevant examples, and characterize completeness in the case of spaces with radial weights on balanced domains.