{
  "id": "1205.2525",
  "version": "v2",
  "published": "2012-05-11T13:57:44.000Z",
  "updated": "2012-05-21T02:37:12.000Z",
  "title": "Sobolev Extension By Linear Operators",
  "authors": [
    "Charles L. Fefferman",
    "Arie Israel",
    "Garving K. Luli"
  ],
  "comment": "98 pages",
  "categories": [
    "math.CA"
  ],
  "abstract": "Let $L^{m,p}(\\R^n)$ be the Sobolev space of functions with $m^{th}$ derivatives lying in $L^p(\\R^n)$. Assume that $n< p < \\infty$. For $E \\subset \\R^n$, let $L^{m,p}(E)$ denote the space of restrictions to $E$ of functions in $L^{m,p}(\\R^n)$. We show that there exists a bounded linear map $T : L^{m,p}(E) \\rightarrow L^{m,p}(\\R^n)$ such that, for any $f \\in L^{m,p}(E)$, we have $Tf = f$ on $E$. We also give a formula for the order of magnitude of $\\|f\\|_{L^{m,p}(E)}$ for a given $f : E \\rightarrow \\R$ when $E$ is finite.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-05-21T02:37:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B99"
    ],
    "keywords": [
      "linear operators",
      "sobolev extension",
      "bounded linear map",
      "sobolev space",
      "restrictions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 98,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1205.2525F"
    }
  }
}