{
  "id": "1201.4708",
  "version": "v1",
  "published": "2012-01-23T13:21:55.000Z",
  "updated": "2012-01-23T13:21:55.000Z",
  "title": "Sobolev spaces and Lagrange interpolation",
  "authors": [
    "Bogdan Bojarski"
  ],
  "comment": "12 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this short paper the discussion of the pointwise characterization of functions $f$ in the Sobolev space $W^{m,p}(\\R^n)$ given in the recent paper (Bojarski) is supplemented in \\SS1 by a direct, essentially geometric, proof of the novel inequality (for $m>1$), appearing in Bojarski apparently for the first time, and involving the use of the $m$-th difference of the function $f$. Moreover in \\SS2 some additional comments to the text in Bojarski are given and a natural class of Sobolev spaces in domains $G$ in $\\R^n$ is defined. \\SS3 contains some final remarks.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-01-23T13:21:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46E35"
    ],
    "keywords": [
      "sobolev space",
      "lagrange interpolation",
      "final remarks",
      "short paper",
      "first time"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1201.4708B"
    }
  }
}