{
  "id": "1602.04997",
  "version": "v1",
  "published": "2016-02-16T11:56:46.000Z",
  "updated": "2016-02-16T11:56:46.000Z",
  "title": "Hardy-type inequalities for fractional powers of the Dunkl--Hermite operator",
  "authors": [
    "Ó. Ciaurri",
    "L. Roncal",
    "S. Thangavelu"
  ],
  "comment": "24 pages",
  "categories": [
    "math.CA",
    "math.FA"
  ],
  "abstract": "We prove Hardy-type inequalities for a fractional Dunkl--Hermite operator which incidentally give Hardy inequalities for the fractional harmonic oscillator as well. The idea is to use $h$-harmonic expansions to reduce the problem in the Dunkl--Hermite context to the Laguerre setting. Then, we push forward a technique based on a non-local ground representation, initially developed by R. L. Frank, E. H. Lieb and R. Seiringer in the Euclidean setting, to get a Hardy inequality for the fractional-type Laguerre operator. The above-mentioned method is shown to be adaptable to an abstract setting, whenever there is a \"good\" spectral theorem and an integral representation for the fractional operators involved.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-02-16T11:56:46.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hardy-type inequalities",
      "fractional powers",
      "hardy inequality",
      "non-local ground representation",
      "fractional harmonic oscillator"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160204997C"
    }
  }
}