{
  "id": "1408.5718",
  "version": "v1",
  "published": "2014-08-25T10:53:18.000Z",
  "updated": "2014-08-25T10:53:18.000Z",
  "title": "Lebesgue points via the Poincaré inequality",
  "authors": [
    "Nijjwal Karak",
    "Pekka Koskela"
  ],
  "comment": "16 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "In this article, we show that in a $Q$-doubling space $(X,d,\\mu),$ $Q>1,$ which satisfies a chain condition, if we have a $Q$-Poincar\\'e inequality for a pair of functions $(u,g)$ where $g\\in L^Q(X),$ then $u$ has Lebesgue points $H^h$-a.e. for $h(t)=\\log^{1-Q-\\epsilon}(1/t).$ We also discuss how the existence of Lebesgue points follows for $u\\in W^{1,Q}(X)$ where $(X,d,\\mu)$ is a complete $Q$-doubling space supporting a $Q$-Poincar\\'e inequality for $Q>1.$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-08-25T10:53:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46E35",
      "28A78",
      "28A15"
    ],
    "keywords": [
      "lebesgue points",
      "poincare inequality",
      "doubling space",
      "chain condition"
    ],
    "publication": {
      "doi": "10.1007/s11425-015-5001-9",
      "journal": "Science in China A: Mathematics",
      "year": 2015,
      "month": "Aug",
      "volume": 58,
      "number": 8,
      "pages": 1697
    },
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015ScChA..58.1697K"
    }
  }
}