{
  "id": "0802.3138",
  "version": "v2",
  "published": "2008-02-21T15:48:48.000Z",
  "updated": "2008-11-24T20:05:12.000Z",
  "title": "Convergence of weighted polynomial multiple ergodic averages",
  "authors": [
    "Qing Chu"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "We study here weighted polynomial multiple ergodic averages. A sequence of weights is called universally good if any polynomial multiple ergodic average with this sequence of weights converges in $L^{2}$. We find a necessary condition and show that for any bounded measurable function $\\phi$ on an ergodic system, the sequence $\\phi(T^{n}x)$ is universally good for almost every $x$. The linear case was understood by Host and Kra.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-11-24T20:05:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37A05",
      "37A30"
    ],
    "keywords": [
      "weighted polynomial multiple ergodic averages",
      "convergence",
      "weights converges",
      "necessary condition",
      "ergodic system"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0802.3138C"
    }
  }
}