Compactness in the spaces of functions of bounded variation

2022/12/01 by Gulgowski, Jacek
#26A45 #46B50 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2212.00649

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 Λ-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].

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