{
  "id": "1708.09733",
  "version": "v1",
  "published": "2017-08-31T14:17:15.000Z",
  "updated": "2017-08-31T14:17:15.000Z",
  "title": "Riesz potential and maximal function for Dunkl transform",
  "authors": [
    "D. V. Gorbachev",
    "V. I. Ivanov",
    "S. Yu. Tikhonov"
  ],
  "comment": "25 pages",
  "categories": [
    "math.CA"
  ],
  "abstract": "We study weighted $(L^p, L^q)$-boundedness properties of Riesz potentials and fractional maximal functions for the Dunkl transform. In particular, we obtain the weighted Hardy-Littlewood-Sobolev type inequality and weighted week $(L^1, L^q)$ estimate. We find a sharp constant in the weighted $L^p$-inequality, generalizing the results of W. Beckner and S. Samko.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-08-31T14:17:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B10",
      "33C45",
      "33C52"
    ],
    "keywords": [
      "dunkl transform",
      "riesz potential",
      "fractional maximal functions",
      "weighted hardy-littlewood-sobolev type inequality",
      "sharp constant"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}