{
  "id": "0901.0932",
  "version": "v1",
  "published": "2009-01-07T21:17:38.000Z",
  "updated": "2009-01-07T21:17:38.000Z",
  "title": "Convergence and divergence of averages along subsequences in certain Orlicz spaces",
  "authors": [
    "C. M. Wedrychowicz"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "The classical theorem of Birkhoff states that the $T^N f(x) = (1/N)\\sum_{k=0}^{N-1} f(\\sigma^k x)$ converges almost everywhere for $x\\in X$ and $f\\in L^{1}(X)$, where $\\sigma$ is a measure preserving transformation of a probability measure space $X$. It was shown that there are operators of the form $T^N f(x)=(1/N)\\sum_{k=0}^{N-1}f(\\sigma^{n_k}x)$ for a subsequence $\\{n_k\\}$ of the positive integers that converge in some $L^p$ spaces while diverging in others. The topic of this talk will examine this phenomenon in the class of Orlicz spaces $\\{L{Log}^\\beta L:\\beta>0\\}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-01-07T21:17:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "orlicz spaces",
      "subsequence",
      "divergence",
      "convergence",
      "probability measure space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}