{
  "id": "1104.1549",
  "version": "v3",
  "published": "2011-04-08T11:30:22.000Z",
  "updated": "2012-03-16T13:01:28.000Z",
  "title": "New characterizations of Hajłasz-Sobolev type spaces with variable exponent on metric measure spaces",
  "authors": [
    "B. Cekic",
    "R. A. Mashiyev"
  ],
  "comment": "This paper has been withdrawn by the author",
  "categories": [
    "math.FA"
  ],
  "abstract": "In this article, we introduce classes of functions whose increment is controlled by the measure of a ball containing the corresponding points and a nonnegative function p(.) that is summable with respect to measure. These classes of functions can be considered as spaces with variable smoothness depending on the structure of the measure in a neighborhood of a given point. Moreover, we present several descriptions generalized classes of variable exponent Haj{\\l}asz-Sobolev type on metric measure spaces by various maximal functions and we establish the equivalence between them.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2012-03-16T13:01:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46E35",
      "28A78",
      "28A80",
      "42B20",
      "46E30"
    ],
    "keywords": [
      "metric measure spaces",
      "hajłasz-sobolev type spaces",
      "variable exponent",
      "characterizations",
      "descriptions generalized classes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1104.1549C"
    }
  }
}