{
  "id": "1409.0679",
  "version": "v1",
  "published": "2014-09-02T12:22:50.000Z",
  "updated": "2014-09-02T12:22:50.000Z",
  "title": "On the boundedness of singular integrals in Morrey spaces and its preduals",
  "authors": [
    "Marcel Rosenthal",
    "Hans-Jürgen Schmeißer"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "We reduce the boundedness of operators in Morrey spaces $L_p^r({\\mathbb R}^n)$, its preduals, $H^{\\varrho}L_p ({\\mathbb R}^n)$, and their preduals $\\overset{\\circ}{L}{}^r_p({\\mathbb R}^n)$ to the boundedness of the appropriate operators in Lebesgue spaces, $L_p({\\mathbb R}^n)$. Hereby, we need a weak condition with respect to the operators which is satisfied for a large set of classical operators of harmonic analysis including singular integral operators and the Hardy-Littlewood maximal function. The given vector-valued consideration of these issues is a key ingredient for various applications in harmonic analysis.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-09-02T12:22:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B25",
      "46E35",
      "42B35",
      "46E30",
      "42B15",
      "42B20"
    ],
    "keywords": [
      "morrey spaces",
      "boundedness",
      "harmonic analysis",
      "singular integral operators",
      "hardy-littlewood maximal function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1409.0679R"
    }
  }
}