{
  "id": "2001.03459",
  "version": "v1",
  "published": "2020-01-08T22:32:56.000Z",
  "updated": "2020-01-08T22:32:56.000Z",
  "title": "Composition operator into the space of function of bounded variation",
  "authors": [
    "Luděk Kleprlík"
  ],
  "comment": "arXiv admin note: substantial text overlap with arXiv:2001.01657",
  "categories": [
    "math.AP"
  ],
  "abstract": "Let $\\Omega_1, \\Omega_2\\subset \\mathbb R^n$ and $1\\leq p <\\infty$. We study the optimal conditions on a homeomorphism $f:\\Omega_1$ onto $\\Omega_2$ which guarantee that the composition $u\\circ f$ belongs to the space $BV(\\Omega_1)$ for every $u\\in W^{1,p}(\\Omega_2)$. We show that the sufficient and necessary condition is an existence of a function $K(y)\\in L^{p'}(\\Omega_2)$ such that $|Df|(f^{-1}(A))\\leq \\int_A K(y)\\,dy$ for all Borel sets $A$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-01-08T22:32:56.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "composition operator",
      "bounded variation",
      "optimal conditions",
      "necessary condition",
      "borel sets"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}