Compactness in the spaces of functions of bounded variation
Functional Analysis
2022-12-02 v1
Abstract
Recently the characterization of the compactness in the space of functions of bounded Jordan variation was given. Here, certain generalizations of this result are given for the spaces of functions of bounded Waterman -variation, Young -variation and integral variation. It appears that on the compact sets the norm is uniformly approximated by certain seminorms induced by the selection of finitely many intervals in .
Keywords
Cite
@article{arxiv.2212.00649,
title = {Compactness in the spaces of functions of bounded variation},
author = {Jacek Gulgowski},
journal= {arXiv preprint arXiv:2212.00649},
year = {2022}
}