{
  "id": "math/0311538",
  "version": "v3",
  "published": "2003-11-28T20:25:57.000Z",
  "updated": "2004-03-09T15:10:17.000Z",
  "title": "Maximal functions associated with Fourier multipliers of Mikhlin-H\"ormander type",
  "authors": [
    "Michael Christ",
    "Loukas Grafakos",
    "Petr Honzik",
    "Andreas Seeger"
  ],
  "comment": "Final version with improved differentiability assumptions on the multipliers. To appear in Mathematische Zeitschrift",
  "journal": "Mathematische Zeitschrift, 249 (2005), 223-240.",
  "categories": [
    "math.CA"
  ],
  "abstract": "We show that maximal operators formed by dilations of Mikhlin-H\"ormander multipliers are typically not bounded on $L^p(R^d)$. We also give rather weak conditions in terms of the decay of such multipliers under which $L^p$ boundedness of the maximal operators holds.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2004-03-09T15:10:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B25",
      "42B15"
    ],
    "keywords": [
      "maximal functions",
      "fourier multipliers",
      "ormander type",
      "maximal operators holds",
      "ormander multipliers"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math.....11538C"
    }
  }
}