{
  "id": "1406.1637",
  "version": "v1",
  "published": "2014-06-06T10:47:33.000Z",
  "updated": "2014-06-06T10:47:33.000Z",
  "title": "Local maximal operators on fractional Sobolev spaces",
  "authors": [
    "Hannes Luiro",
    "Antti V. Vähäkangas"
  ],
  "categories": [
    "math.CA",
    "math.FA"
  ],
  "abstract": "In this note we establish the boundedness properties of local maximal operators $M_G$ on the fractional Sobolev spaces $W^{s,p}(G)$ whenever $G$ is an open set in $\\mathbb{R}^n$, $0<s<1$ and $1<p<\\infty$. As an application, we characterize the fractional $(s,p)$-Hardy inequality on a bounded open set $G$ by a Maz'ya-type testing condition localized to Whitney cubes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-06-06T10:47:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B25",
      "46E35",
      "47H99"
    ],
    "keywords": [
      "local maximal operators",
      "fractional sobolev spaces",
      "mazya-type testing condition",
      "boundedness properties",
      "bounded open set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1406.1637L"
    }
  }
}