English

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 BV([0,1])BV([0,1]) of functions of bounded Jordan variation was given. Here, certain generalizations of this result are given for the spaces of functions of bounded Waterman Λ\Lambda-variation, Young Φ\Phi-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 [0,1][0,1].

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}
}