{
  "id": "math/0105159",
  "version": "v1",
  "published": "2001-05-18T17:50:22.000Z",
  "updated": "2001-05-18T17:50:22.000Z",
  "title": "Carleson's theorem with quadratic phase",
  "authors": [
    "Michael Lacey"
  ],
  "journal": "Studia Math. 153 (2002), no. 3, 249--267",
  "categories": [
    "math.CA"
  ],
  "abstract": "Carleson's theorem on the pointwise convergence of Fourier series provides bounds for a maximal operator, with the maximum taken over all choices of linear functions of a phase argument. We extend this to all quadratic choices of phase functions. Specifically, we show that the maximal operator below maps $L^p$ into itself for $1<p<\\infty$. $$ \\sup_a \\sup_b |\\int e^{i(ay^2+by)}f(x-y)dy/y| $$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2001-05-18T17:50:22.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "carlesons theorem",
      "quadratic phase",
      "maximal operator",
      "quadratic choices",
      "phase argument"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001math......5159L"
    }
  }
}