{
  "id": "1011.2032",
  "version": "v1",
  "published": "2010-11-09T10:43:32.000Z",
  "updated": "2010-11-09T10:43:32.000Z",
  "title": "Rubio de Francia's extrapolation theory: estimates for the distribution function",
  "authors": [
    "María J. Carro",
    "Javier Soria",
    "Rodolfo H. Torres"
  ],
  "comment": "29 pages",
  "doi": "10.1112/jlms/jdr056",
  "categories": [
    "math.CA",
    "math.FA"
  ],
  "abstract": "Let $T$ be an arbitrary operator bounded from $L^{p_0}(w)$ into $L^{p_0, \\infty}(w)$ for every weight $w$ in the Muckenhoupt class $A_{p_0}$. It is proved in this article that the distribution function of $Tf$ with respect to any weight $u$ can be essentially majorized by the distribution function of $Mf$ with respect to $u$ (plus an integral term easy to control). As a consequence, well-known extrapolation results, including results in a multilinear setting, can be obtained with very simple proofs. New applications in extrapolation for two-weight problems and estimates on rearrangement invariant spaces are established too.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-11-09T10:43:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B35",
      "46E30"
    ],
    "keywords": [
      "francias extrapolation theory",
      "distribution function",
      "rearrangement invariant spaces",
      "well-known extrapolation results",
      "integral term"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1011.2032C"
    }
  }
}