{
  "id": "1301.1524",
  "version": "v2",
  "published": "2013-01-08T13:32:40.000Z",
  "updated": "2013-03-20T02:49:09.000Z",
  "title": "Positivity of $|p|^a|q|^b+|q|^b|p|^a$",
  "authors": [
    "Li Chen",
    "Heinz Siedentop"
  ],
  "comment": "6 pages",
  "categories": [
    "math-ph",
    "math.FA",
    "math.MP"
  ],
  "abstract": "We show that $$J_{a,b,n}:=\\frac12(|p|^a|q|^b+|q|^b|p|^a)$$ is positive, if $n\\geq b+a$. (Here $q$ is the multiplication by $x$ and $p:= \\mathrm{i}^{-1}\\nabla$.) Furthermore we show that it generalizes the generalized Hardy inequalities for the fractional Laplacians.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-03-20T02:49:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A63",
      "26D10",
      "81Q10"
    ],
    "keywords": [
      "positivity",
      "generalized hardy inequalities",
      "fractional laplacians"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}