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arXiv · 1607.08640

A note on completeness of weighted normed spaces of analytic functions

José Bonet·Dragan Vukotić
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Abstract

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 under the canonical sup-seminorm. We obtain both some necessary and some sufficient conditions in terms of the weight $v$, exhibit several relevant examples, and characterize completeness in the case of spaces with radial weights on balanced domains.

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José Bonet, Dragan Vukotić. 2016-07-28. A note on completeness of weighted normed spaces of analytic functions. https://doi.org/10.1007/s00025-017-0696-2

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