{
  "id": "0902.4645",
  "version": "v2",
  "published": "2009-02-26T17:31:55.000Z",
  "updated": "2009-10-19T16:50:24.000Z",
  "title": "Pointwise Convergence of Ergodic Averages in Orlicz Spaces",
  "authors": [
    "Andrew Parrish"
  ],
  "categories": [
    "math.DS",
    "math.FA"
  ],
  "abstract": "We show that for each Orlicz space properly contained in L^1 there is a sequence along which the ergodic averages converge for functions in the Orlicz space, but diverge for all f in L^1. This extends the work of K. Reinhold, who, building on the work of A. Bellow,constructed a sequence for which the averages converge a.e. for every f in L^p, p>q, but diverge for some f in L^q. Our method, introduced by Bellow and extended by Reinhold and M. Wierdl, is perturbation.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-10-19T16:50:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37A05",
      "37A45"
    ],
    "keywords": [
      "pointwise convergence",
      "ergodic averages converge",
      "orlicz space",
      "perturbation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0902.4645P"
    }
  }
}