{
  "id": "1904.08725",
  "version": "v1",
  "published": "2019-04-18T12:28:44.000Z",
  "updated": "2019-04-18T12:28:44.000Z",
  "title": "Rellich, Gagliardo-Nirenberg and Caffarelli-Kohn-Nirenberg inequalities for Dunkl operators and applications",
  "authors": [
    "Andrei Velicu",
    "Nurgissa Yessirkegenov"
  ],
  "comment": "27 pages",
  "categories": [
    "math.AP",
    "math.FA"
  ],
  "abstract": "In this paper we obtain weighted higher order Rellich, weighted Gagliardo-Nirenberg, Caffarelli-Kohn-Nirenberg inequalities and the uncertainty principle for Dunkl operators. Moreover, we introduce an extension of the classical Caffarelli-Kohn-Nirenberg inequalities. Furthermore, we give an application of Gagliardo-Nirenberg inequality to the Cauchy problem for the nonlinear damped wave equations for the Dunkl Laplacian.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-04-18T12:28:44.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "dunkl operators",
      "application",
      "weighted higher order rellich",
      "nonlinear damped wave equations",
      "classical caffarelli-kohn-nirenberg inequalities"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}