{
  "id": "math/0601213",
  "version": "v2",
  "published": "2006-01-10T12:41:25.000Z",
  "updated": "2006-11-02T22:31:46.000Z",
  "title": "On a Lipschitz Variant of the Kakeya Maximal Function",
  "authors": [
    "Michael Lacey",
    "Xiaochun Li"
  ],
  "comment": "12 pages. The L^2 estimate for the maximal function in this paper is correct. A claimed L^p inequality, for 1<p<2, had an incomplete proof",
  "categories": [
    "math.CA"
  ],
  "abstract": "In a prior work [Hilbert transform along smooth families of lines math.CA/0310345] the authors introduced a variant of the Kakeya maximal function associated with Lipschitz maps from the plane into the unit circle. In this paper, we improve the known estimates for this maximal operator--and raise the conjecture that the bounds established are optimal.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2006-11-02T22:31:46.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "lipschitz variant",
      "maximal operator-and raise",
      "smooth families",
      "lines math",
      "prior work"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......1213L"
    }
  }
}