{
  "id": "1308.3606",
  "version": "v2",
  "published": "2013-08-16T11:29:25.000Z",
  "updated": "2013-10-04T20:04:52.000Z",
  "title": "On fractional Laplacians",
  "authors": [
    "Roberta Musina",
    "Alexander I. Nazarov"
  ],
  "comment": "14 pages; this version is considerably enlarged",
  "categories": [
    "math.AP"
  ],
  "abstract": "We compare two natural types of fractional Laplacians $(-\\Delta)^s$, \"Navier\" and \"Dirichlet\" ones. We show that for $0<s<1$ their difference is positive definite and positivity preserving. Then we prove the coincidence of the Sobolev constants for these two fractional Laplacians.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-10-04T20:04:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A63",
      "35A23"
    ],
    "keywords": [
      "fractional laplacians",
      "natural types",
      "sobolev constants",
      "difference"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1308.3606M"
    }
  }
}