{
  "id": "0809.4044",
  "version": "v1",
  "published": "2008-09-23T22:56:18.000Z",
  "updated": "2008-09-23T22:56:18.000Z",
  "title": "On the regularity of maximal operators",
  "authors": [
    "Emanuel Carneiro",
    "Diego Moreira"
  ],
  "comment": "10 pages",
  "journal": "Proc. Amer. Math. Soc. 136 (2008), 4395-4404",
  "doi": "10.1090/S0002-9939-08-09515-4",
  "categories": [
    "math.CA"
  ],
  "abstract": "We study the regularity of the bilinear maximal operator when applied to Sobolev functions, proving that it maps $W^{1,p}(\\mathbb{R}) \\times W^{1,q}(\\mathbb{R}) \\to W^{1,r}(\\mathbb{R})$ with $1 <p,q < \\infty$ and $r\\geq 1$, boundedly and continuously. The same result holds on $\\mathbb{R}^n$ when $r>1$. We also investigate the almost everywhere and weak convergence under the action of the classical Hardy-Littlewood maximal operator, both in its global and local versions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-09-23T22:56:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B25",
      "54C08",
      "46E35"
    ],
    "keywords": [
      "regularity",
      "bilinear maximal operator",
      "classical hardy-littlewood maximal operator",
      "sobolev functions",
      "result holds"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AMS",
      "journal": "Proc. Amer. Math. Soc."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0809.4044C"
    }
  }
}