{
  "id": "1509.02068",
  "version": "v1",
  "published": "2015-09-07T15:00:46.000Z",
  "updated": "2015-09-07T15:00:46.000Z",
  "title": "The Besov Capacity In Metric Spaces",
  "authors": [
    "Juho Nuutinen"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "We study a capacity theory based on a definition of Haj{\\l} asz-Besov functions. We prove several properties of this capacity in the general setting of a metric space equipped with a doubling measure. The main results of the paper are lower bound and upper bound estimates for the capacity in terms of a modified Netrusov-Hausdorff content. Important tools are $\\gamma$-medians, for which we also prove a new version of a Poincar\\'e type inequality.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-09-07T15:00:46.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "metric space",
      "besov capacity",
      "poincare type inequality",
      "upper bound estimates",
      "important tools"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150902068N"
    }
  }
}