{
  "id": "1310.6604",
  "version": "v2",
  "published": "2013-10-24T13:17:49.000Z",
  "updated": "2013-12-30T11:33:31.000Z",
  "title": "On the Riesz potential and its commutators on generalized Orlicz-Morrey spaces",
  "authors": [
    "Vagif S. Guliyev",
    "Fatih Deringoz"
  ],
  "comment": "23 pages. J. Funct. Spaces Appl.(to appear)",
  "categories": [
    "math.FA"
  ],
  "abstract": "We consider generalized Orlicz-Morrey spaces $M_{\\Phi,\\varphi}(\\Rn)$ including their weak versions $WM_{\\Phi,\\varphi}(\\Rn)$. In these spaces we prove the boundedness of the Riesz potential from $M_{\\Phi,\\varphi_1}(\\Rn)$ to $M_{\\Psi,\\varphi_2}(\\Rn)$ and from $M_{\\Phi,\\varphi_1}(\\Rn)$ to $WM_{\\Psi,\\varphi_2}(\\Rn)$. As applications of those results, the boundedness of the commutators of the Riesz potential on generalized Orlicz-Morrey space is also obtained. In all the cases the conditions for the boundedness are given either in terms of Zygmund-type integral inequalities on $(\\varphi_{1},\\varphi_{2})$, which do not assume any assumption on monotonicity of $\\varphi_{1}(x,r)$, $\\varphi_{2}(x,r)$ in r.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-12-30T11:33:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B20",
      "42B25",
      "42B35",
      "46E30"
    ],
    "keywords": [
      "generalized orlicz-morrey space",
      "riesz potential",
      "commutators",
      "boundedness",
      "zygmund-type integral inequalities"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1310.6604G"
    }
  }
}