{
  "id": "0808.2390",
  "version": "v1",
  "published": "2008-08-18T13:49:21.000Z",
  "updated": "2008-08-18T13:49:21.000Z",
  "title": "Weighted Hardy and singular operators in Morrey spaces",
  "authors": [
    "Natasha Samko"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "We study the weighted boundedness of the Cauchy singular integral operator $S_\\Gm$ in Morrey spaces $L^{p,\\lambda}(\\Gm)$ on curves satisfying the arc-chord condition, for a class of \"radial type\" almost monotonic weights. The non-weighted boundedness is shown to hold on an arbitrary Carleson curve. We show that the weighted boundedness is reduced to the boundedness of weighted Hardy operators in Morrey spaces $L^{p,\\lambda}(0,\\ell), \\ell>0$. We find conditions for weighted Hardy operators to be bounded in Morrey spaces. To cover the case of curves we also extend the boundedness of the Hardy-Littlewood maximal operator in Morrey spaces, known in the Euclidean setting, to the case of Carleson curves. Key words and phrases: Morrey space, singular operator, Hardy operator, Hardy-Littlewood maximal operator, weighted estimate.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-08-18T13:49:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46E30",
      "42B35",
      "42B25",
      "47B38"
    ],
    "keywords": [
      "morrey space",
      "singular operator",
      "hardy-littlewood maximal operator",
      "weighted hardy operators",
      "cauchy singular integral operator"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0808.2390S"
    }
  }
}