{
  "id": "1011.2937",
  "version": "v2",
  "published": "2010-11-12T15:05:50.000Z",
  "updated": "2010-12-17T07:48:16.000Z",
  "title": "Boundedness of Calderón-Zygmund Operators on Non-homogeneous Metric Measure Spaces",
  "authors": [
    "Tuomas Hytönen",
    "Suile Liu",
    "Dachun Yang",
    "Dongyong Yang"
  ],
  "comment": "Canad. J. Math. (to appear)",
  "categories": [
    "math.CA"
  ],
  "abstract": "Let $({\\mathcal X}, d, \\mu)$ be a separable metric measure space satisfying the known upper doubling condition, the geometrical doubling condition and the non-atomic condition that $\\mu(\\{x\\})=0$ for all $x\\in{\\mathcal X}$. In this paper, we show that the boundedness of a Calder\\'on-Zygmund operator $T$ on $L^2(\\mu)$ is equivalent to that of $T$ on $L^p(\\mu)$ for some $p\\in (1, \\infty)$, and that of $T$ from $L^1(\\mu)$ to $L^{1,\\,\\infty}(\\mu).$ As an application, we prove that if $T$ is a Calder\\'on-Zygmund operator bounded on $L^2(\\mu)$, then its maximal operator is bounded on $L^p(\\mu)$ for all $p\\in (1, \\infty)$ and from the space of all complex-valued Borel measures on ${\\mathcal X}$ to $L^{1,\\,\\infty}(\\mu)$. All these results generalize the corresponding results of Nazarov et al. on metric spaces with measures satisfying the so-called polynomial growth condition.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-12-17T07:48:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B20",
      "42B25",
      "30L99"
    ],
    "keywords": [
      "non-homogeneous metric measure spaces",
      "calderón-zygmund operators",
      "metric measure space satisfying",
      "boundedness",
      "calderon-zygmund operator"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1011.2937H"
    }
  }
}