{
  "id": "2212.00649",
  "version": "v1",
  "published": "2022-12-01T16:51:59.000Z",
  "updated": "2022-12-01T16:51:59.000Z",
  "title": "Compactness in the spaces of functions of bounded variation",
  "authors": [
    "Jacek Gulgowski"
  ],
  "categories": [
    "math.FA"
  ],
  "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 $\\Lambda$-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 $[0,1]$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-12-01T16:51:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B50",
      "26A45"
    ],
    "keywords": [
      "bounded variation",
      "compactness",
      "bounded jordan variation",
      "integral variation",
      "compact sets"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}