{
  "id": "2001.01657",
  "version": "v1",
  "published": "2020-01-06T16:44:34.000Z",
  "updated": "2020-01-06T16:44:34.000Z",
  "title": "Composition operator for functions of bounded variation",
  "authors": [
    "Luděk Kleprlík"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We study the optimal conditions on a homeomorphism $f:\\Omega\\subset \\R^n\\to \\R^n$ to guarantee that the composition $u\\circ f$ belongs to the space of functions of bounded variation for every function $u$ of bounded variation. We show that a sufficient and necessary condition is the existence of a constant $K$ such that $|Df|(f^{-1}(A))\\leq K\\Ln(A)$ for all Borel sets $A$. We also characterize homeomorphisms which maps sets of finite perimeter to sets of finite perimeter. Towards these results we study when $f^{-1}$ maps sets of measure zero onto sets of measure zero (i.e. $f$ satisfies the Lusin $(N^{-1})$ condition).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-01-06T16:44:34.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "bounded variation",
      "composition operator",
      "maps sets",
      "finite perimeter",
      "measure zero"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}