{
  "id": "1011.0667",
  "version": "v2",
  "published": "2010-11-02T16:37:17.000Z",
  "updated": "2010-11-27T19:28:25.000Z",
  "title": "A new characterization of Sobolev spaces on $\\mathbb{R}^n$",
  "authors": [
    "Roc Alabern",
    "Joan Mateu",
    "Joan Verdera"
  ],
  "comment": "Two references added. Some statements have been improved and proofs made clearer. Typos corrected",
  "categories": [
    "math.CA",
    "math.AP",
    "math.FA"
  ],
  "abstract": "In this paper we present a new characterization of Sobolev spaces on Euclidian spaces ($\\mathbb{R}^n$). Our characterizing condition is obtained via a quadratic multiscale expression which exploits the particular symmetry properties of Euclidean space. An interesting feature of our condition is that depends only on the metric of $\\mathbb{R}^n$ and the Lebesgue measure, so that one can define Sobolev spaces of any order of smoothness on any metric measure space.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-11-27T19:28:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B35",
      "42B99",
      "31B99"
    ],
    "keywords": [
      "characterization",
      "metric measure space",
      "define sobolev spaces",
      "quadratic multiscale expression",
      "lebesgue measure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1011.0667A"
    }
  }
}