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- Title
Compactness in the spaces of functions of bounded variation.
- Authors
Gulgowski, Jacek
- Abstract
Recently, the characterization of the compactness in the space 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 Μ-variation, Young Φ-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].
- Subjects
JORDAN; FUNCTIONS of bounded variation; FUNCTION spaces; ORLICZ spaces
- Publication
Journal of Analysis & Its Applications / Zeitschrift für Analysis & ihre Anwendungen, 2023, Vol 42, Issue 3/4, p283
- ISSN
0232-2064
- Publication type
Article
- DOI
10.4171/ZAA/1733