Jacek Gulgowski
Published 2022-12-01Version 1
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 $\Lambda$-variation, Young $\Phi$-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 $[0,1]$.
Defect of compactness in spaces of bounded variation
On functions of bounded variation on convex domains in Hilbert spaces
Extensions and traces of functions of bounded variation on metric spaces
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