{
  "id": "math/0601192",
  "version": "v1",
  "published": "2006-01-09T20:55:00.000Z",
  "updated": "2006-01-09T20:55:00.000Z",
  "title": "Wiener-Wintner for Hilbert Transform",
  "authors": [
    "Michael Lacey",
    "Erin Terwilleger"
  ],
  "comment": "Submitted to Arkiv",
  "categories": [
    "math.CA",
    "math.DS"
  ],
  "abstract": "We prove the following extension of the Wiener--Wintner Theorem in Ergodic Theor and the Carleson Theorem on pointwise convergence of Fourier series: For all measure preserving flows $ (X,\\mu , T_t)$ and $ f\\in L^p (X,\\mu)$, there is a set $X_f\\subset X $ of probability one, so that for all $x\\in X_f$ we have \\begin{equation*} \\lim _{s\\downarrow0} \\int _{s<\\abs t<1/s} \\operatorname e ^{i \\theta t} f(\\operatorname T_tx)\\; \\frac{dt}t \\qquad \\text{exists for all $\\theta$.} \\end{equation*} The proof is by way of establishing an appropriate oscillation inequality which is itself an extension of Carleson's theorem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-01-09T20:55:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hilbert transform",
      "appropriate oscillation inequality",
      "carlesons theorem",
      "ergodic theor",
      "carleson theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......1192L"
    }
  }
}