{
  "id": "1310.6852",
  "version": "v1",
  "published": "2013-10-25T08:48:54.000Z",
  "updated": "2013-10-25T08:48:54.000Z",
  "title": "Some aspects of harmonic analysis related to Gegenbauer expansions on the half-line",
  "authors": [
    "Vagif S. Guliyev",
    "Elman J. Ibrahimov"
  ],
  "comment": "44 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "In this paper we consider the generalized shift operator, generated by the Gegenbauer differential operator $$ G =\\left(x^2-1\\right)^{\\frac{1}{2}-\\lambda} \\frac{d}{dx} \\left(x^2-1\\right)^{\\lambda+\\frac{1}{2}}\\frac{d}{dx}. $$ Maximal function ($ G- $ maximal function), generated by the Gegenbauer differential operator $ G $ is investigated. The $ L_{p,\\lambda} $ -boundedness for the $ G- $ maximal function is obtained. The concept of potential of Riesz-Gegenbauer is introduced and for it the theorem of Sobolev type is proved.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-10-25T08:48:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B20",
      "42B25",
      "42B35"
    ],
    "keywords": [
      "harmonic analysis",
      "gegenbauer expansions",
      "maximal function",
      "gegenbauer differential operator",
      "generalized shift operator"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 44,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1310.6852G"
    }
  }
}