{
  "id": "1204.2208",
  "version": "v1",
  "published": "2012-04-10T16:17:41.000Z",
  "updated": "2012-04-10T16:17:41.000Z",
  "title": "Riesz type potential operators in generalized grand Morrey spaces",
  "authors": [
    "Vakhtang Kokilashvili",
    "Alexander Meskhi",
    "Humberto Rafeiro"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:1109.2550",
  "categories": [
    "math.FA"
  ],
  "abstract": "In this paper we introduce generalized grand Morrey spaces in the framework of quasimetric measure spaces, in the spirit of the so-called grand Lebesgue spaces. We prove a kind of reduction lemma which is applicable to a variety of operators to reduce their boundedness in generalized grand Morrey spaces to the corresponding boundedness in Morrey spaces, as a result of this application, we obtain the boundedness of the Hardy-Littlewood maximal operator as well as the boundedness of Calder\\'on-Zygmund potential type operators. Boundedness of Riesz type potential operators are also obtained in the framework of homogeneous and also in the nonhomogeneous case in generalized grand Morrey spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-04-10T16:17:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46E30",
      "42B20",
      "42B25"
    ],
    "keywords": [
      "generalized grand morrey spaces",
      "riesz type potential operators",
      "boundedness",
      "calderon-zygmund potential type operators",
      "quasimetric measure spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1204.2208K"
    }
  }
}