{
  "id": "0810.3073",
  "version": "v1",
  "published": "2008-10-17T06:58:30.000Z",
  "updated": "2008-10-17T06:58:30.000Z",
  "title": "Weighted norm inequalities, off-diagonal estimates and elliptic operators",
  "authors": [
    "Pascal Auscher",
    "José Maria Martell"
  ],
  "comment": "survey for the El Escorial 2008 proceedings",
  "categories": [
    "math.CA",
    "math.AP",
    "math.DG"
  ],
  "abstract": "We give an overview of the generalized Calder\\'on-Zygmund theory for \"non-integral\" singular operators, that is, operators without kernels bounds but appropriate off-diagonal estimates. This theory is powerful enough to obtain weighted estimates for such operators and their commutators with $\\BMO$ functions. $L^p-L^q$ off-diagonal estimates when $p\\le q$ play an important role and we present them. They are particularly well suited to the semigroups generated by second order elliptic operators and the range of exponents $(p,q)$ rules the $L^p$ theory for many operators constructed from the semigroup and its gradient. Such applications are summarized.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-10-17T06:58:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B20",
      "42B25",
      "47A06",
      "35J15",
      "47A60",
      "58J35"
    ],
    "keywords": [
      "weighted norm inequalities",
      "second order elliptic operators",
      "appropriate off-diagonal estimates",
      "kernels bounds",
      "important role"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0810.3073A"
    }
  }
}