{
  "id": "math/0603642",
  "version": "v1",
  "published": "2006-03-28T08:06:16.000Z",
  "updated": "2006-03-28T08:06:16.000Z",
  "title": "Weighted norm inequalities, off-diagonal estimates and elliptic operators. Part III: Harmonic analysis of elliptic operators",
  "authors": [
    "Pascal Auscher",
    "José Maria Martell"
  ],
  "comment": "38 pages. Third of 4 papers",
  "categories": [
    "math.CA",
    "math.AP"
  ],
  "abstract": "This is the third part of a series of four articles on weighted norm inequalities, off-diagonal estimates and elliptic operators. For $L$ in some class of elliptic operators, we study weighted norm $L^p$ inequalities for singular 'non-integral' operators arising from $L$ ; those are the operators $\\phi(L)$ for bounded holomorphic functions $\\phi$, the Riesz transforms $\\nabla L^{-1/2}$ (or $(-\\Delta)^{1/2}L^{-1/2}$) and its inverse $L^{1/2}(-\\Delta)^{-1/2}$, some quadratic functionals $g\\_{L}$ and $G\\_{L}$ of Littlewood-Paley-Stein type and also some vector-valued inequalities such as the ones involved for maximal $L^p$-regularity. For each, we obtain sharp or nearly sharp ranges of $p$ using the general theory for boundedness of Part I and the off-diagonal estimates of Part II. We also obtain commutator results with BMO functions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-03-28T08:06:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B20",
      "42B25",
      "47A60"
    ],
    "keywords": [
      "elliptic operators",
      "weighted norm inequalities",
      "off-diagonal estimates",
      "harmonic analysis",
      "commutator results"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 38,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......3642A"
    }
  }
}