关于解析函数加权赋范空间完备性的注记
泛函分析
2018-10-31 v4
摘要
给定一个定义在复平面区域 上的非负权重 （不必有界或严格正），我们考虑 上所有使得乘积 在 中有界的全纯函数构成的加权空间 ，并研究该空间在典范上确界半范数下何时完备的问题。我们得到了关于权重 的一些必要条件和一些充分条件，展示了若干相关例子，并刻画了在平衡域上具有径向权重的空间情形下的完备性。
引用
@article{arxiv.1607.08640,
title = {A note on completeness of weighted normed spaces of analytic functions},
author = {José Bonet and Dragan Vukotić},
journal= {arXiv preprint arXiv:1607.08640},
year = {2018}
}
备注
20 pages. The title of the first version was confusing and was changed accordingly in the second version. In the third version several misprints have been corrected and some explanations have been clarified and in the fourth version a few minor misprints were corrected