{
  "id": "1812.00212",
  "version": "v1",
  "published": "2018-12-01T15:03:27.000Z",
  "updated": "2018-12-01T15:03:27.000Z",
  "title": "Continuity of composition operators in Sobolev spaces",
  "authors": [
    "Gérard Bourdaud",
    "Madani Moussai"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "We prove that all the composition operators $T_f(g):= f\\circ g$, which take the Adams-Frazier space $W^{m}_{p}\\cap \\dot{W}^{1}_{mp}(\\re^n)$ to itself, are continuous mappings from $W^{m}_{p}\\cap \\dot{W}^{1}_{mp}(\\re^n)$ to itself, for every integer $m\\geq 2$ and every real number $1\\leq p<+\\infty$. The same automatic continuity property holds for Sobolev spaces $W^m_p(\\R)$ for $m\\geq 2$ and $1\\leq p<+\\infty$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-12-01T15:03:27.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "sobolev spaces",
      "composition operators",
      "automatic continuity property holds",
      "adams-frazier space",
      "real number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}