{
  "id": "1104.3237",
  "version": "v1",
  "published": "2011-04-16T13:06:18.000Z",
  "updated": "2011-04-16T13:06:18.000Z",
  "title": "Almost everywhere convergence of convolution products",
  "authors": [
    "Karin Reinhold",
    "Anna Savvopoulou",
    "Christopher Wedrychowicz"
  ],
  "comment": "13 pages, to appear In the Canadian Mathematical Bulletin",
  "categories": [
    "math.CA"
  ],
  "abstract": "Let $(X,\\mathcal{B},m,\\tau)$ be a dynamical system with $\\ds (X,\\mathcal{B},m)$ a probability space and $\\ds \\tau$ an invertible, measure preserving transformation. The present paper deals with the almost everywhere convergence in $\\ds{L}^1(X)$ of a sequence of operators of weighted averages. Almost everywhere convergence follows once we obtain an appropriate maximal estimate and once we provide a dense class where convergence holds almost everywhere. The weights are given by convolution products of members of a sequence of probability measures $\\ds\\{\\nu_i\\}$ defined on $\\ds\\mathbb{Z}$. We then exhibit cases of such averages, where convergence fails.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-04-16T13:06:18.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "convolution products",
      "appropriate maximal estimate",
      "measure preserving transformation",
      "paper deals",
      "probability space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1104.3237R"
    }
  }
}