{
  "id": "0711.1291",
  "version": "v1",
  "published": "2007-11-08T14:49:23.000Z",
  "updated": "2007-11-08T14:49:23.000Z",
  "title": "Convergence of Singular integrals with general measures",
  "authors": [
    "P. Mattila",
    "J. Verdera"
  ],
  "comment": "to appear in J. Eur. Math. Soc",
  "journal": "J. Eur. Math. Soc. (JEMS) 11 (2009), no. 2, 257-271",
  "categories": [
    "math.CA",
    "math.FA"
  ],
  "abstract": "We show that L^2-bounded singular integral in metric spaces with respect to general measures and kernels converge weakly. This implies a kind of average convergence almost everywhere. For measures with zero density we prove the almost everywhere existence of principal values.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-11-08T14:49:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B20"
    ],
    "keywords": [
      "general measures",
      "singular integral",
      "kernels converge",
      "principal values",
      "average convergence"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0711.1291M"
    }
  }
}