{
  "id": "math/0601277",
  "version": "v1",
  "published": "2006-01-12T08:56:51.000Z",
  "updated": "2006-01-12T08:56:51.000Z",
  "title": "Pointwise convergence of the ergodic bilinear Hilbert transform",
  "authors": [
    "Ciprian Demeter"
  ],
  "comment": "28 pages, no figures",
  "categories": [
    "math.CA",
    "math.DS"
  ],
  "abstract": "Let ${\\bf X}=(X, \\Sigma, m, \\tau)$ be a dynamical system. We prove that the bilinear series $\\sideset{}{'}\\sum_{n=-N}^{N}\\frac{f(\\tau^nx)g(\\tau^{-n}x)}{n}$ converges almost everywhere for each $f,g\\in L^{\\infty}(X).$ We also give a proof along the same lines of Bourgain's analog result for averages.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-01-12T08:56:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B20",
      "42B25",
      "37A05"
    ],
    "keywords": [
      "ergodic bilinear hilbert transform",
      "pointwise convergence",
      "bourgains analog result",
      "bilinear series"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......1277D"
    }
  }
}