{
  "id": "1405.6045",
  "version": "v2",
  "published": "2014-05-23T12:44:25.000Z",
  "updated": "2014-10-27T09:32:31.000Z",
  "title": "Boundedness of fractional maximal operator and its commutators on generalized Orlicz-Morrey spaces",
  "authors": [
    "Vagif S. Guliyev",
    "Fatih Deringoz"
  ],
  "comment": "23 pages. Complex Anal. Oper. Theory (to appear). arXiv admin note: substantial text overlap with arXiv:1310.6604",
  "categories": [
    "math.FA"
  ],
  "abstract": "We consider generalized Orlicz-Morrey spaces $M_{\\Phi,\\varphi}(\\mathbb{R}^{n})$ including their weak versions $WM_{\\Phi,\\varphi}(\\mathbb{R}^{n})$. We find the sufficient conditions on the pairs $(\\varphi_{1},\\varphi_{2})$ and $(\\Phi, \\Psi)$ which ensures the boundedness of the fractional maximal operator $M_{\\alpha}$ from $M_{\\Phi,\\varphi_1}(\\mathbb{R}^{n})$ to $M_{\\Psi,\\varphi_2}(\\mathbb{R}^{n})$ and from $M_{\\Phi,\\varphi_1}(\\mathbb{R}^{n})$ to $WM_{\\Psi,\\varphi_2}(\\mathbb{R}^{n})$. As applications of those results, the boundedness of the commutators of the fractional maximal operator $M_{b,\\alpha}$ with $b \\in BMO(\\mathbb{R}^{n})$ on the spaces $M_{\\Phi,\\varphi}(\\mathbb{R}^{n})$ is also obtained. In all the cases the conditions for the boundedness are given in terms of supremal-type inequalities on weights $\\varphi(x,r)$, which do not assume any assumption on monotonicity of $\\varphi(x,r)$ on $r$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-05-23T12:44:25.000Z",
      "comment": "arXiv admin note: substantial text overlap with arXiv:1310.6604",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-10-27T09:32:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B20",
      "42B25",
      "42B35",
      "46E30"
    ],
    "keywords": [
      "fractional maximal operator",
      "generalized orlicz-morrey spaces",
      "boundedness",
      "commutators",
      "weak versions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1405.6045G"
    }
  }
}