{
  "id": "1703.06830",
  "version": "v1",
  "published": "2017-03-20T16:30:02.000Z",
  "updated": "2017-03-20T16:30:02.000Z",
  "title": "Positive $L^p$-bounded Dunkl-type generalized translation operator and its applications",
  "authors": [
    "D. V. Gorbachev",
    "V. I. Ivanov",
    "S. Yu. Tikhonov"
  ],
  "comment": "41 pages",
  "categories": [
    "math.CA"
  ],
  "abstract": "We prove that the spherical mean value of the Dunkl-type generalized translation operator $\\tau^y$ is a positive $L^p$-bounded generalized translation operator $T^t$. As application, we prove the Young inequality for a convolution defined by $T^t$, the $L^p$-boundedness of $\\tau^y$ on a radial functions for $p>2$, the $L^p$-boundedness of the Riesz potential for the Dunkl transform and direct and inverse theorems of approximation theory in $L^p$-spaces with the Dunkl weight.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-03-20T16:30:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B10",
      "33C45",
      "33C52"
    ],
    "keywords": [
      "bounded dunkl-type generalized translation operator",
      "application",
      "bounded generalized translation operator",
      "spherical mean value",
      "young inequality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 41,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}