{
  "id": "2103.06550",
  "version": "v1",
  "published": "2021-03-11T09:24:19.000Z",
  "updated": "2021-03-11T09:24:19.000Z",
  "title": "Optimal Hardy inequality for the fractional Laplacian on $L^p$",
  "authors": [
    "Krzysztof Bogdan",
    "Tomasz Jakubowski",
    "Julia Lenczewska",
    "Katarzyna Pietruska-Pałuba"
  ],
  "comment": "25 pages",
  "categories": [
    "math.AP",
    "math.FA"
  ],
  "abstract": "For the fractional Laplacian we give Hardy inequality which is optimal in $L^p$ for $1<p<\\infty$. As an application, we explicitly characterize the contractivity of the corresponding Feynman-Kac semigroups on $L^p$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-03-11T09:24:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46E35",
      "31C05"
    ],
    "keywords": [
      "optimal hardy inequality",
      "fractional laplacian",
      "corresponding feynman-kac semigroups",
      "application"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}