{
  "id": "1302.0146",
  "version": "v1",
  "published": "2013-02-01T11:21:29.000Z",
  "updated": "2013-02-01T11:21:29.000Z",
  "title": "Boundedness of maximal functions on non-doubling manifolds with ends",
  "authors": [
    "Xuan Thinh Duong",
    "Ji Li",
    "Adam Sikora"
  ],
  "categories": [
    "math.AP",
    "math.FA"
  ],
  "abstract": "Let $M$ be a manifold with ends constructed in \\cite{GS} and $\\Delta$ be the Laplace-Beltrami operator on $M$. In this note, we show the weak type $(1,1)$ and $L^p$ boundedness of the Hardy-Littlewood maximal function and of the maximal function associated with the heat semigroup $\\M_\\Delta f(x)=\\sup_{t> 0} |\\exp (-t\\Delta)f(x)| $ on $L^p(M)$ for $1 < p \\le \\infty$. The significance of these results comes from the fact that $M$ does not satisfies the doubling condition.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-02-01T11:21:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B15",
      "35P99"
    ],
    "keywords": [
      "non-doubling manifolds",
      "boundedness",
      "hardy-littlewood maximal function",
      "weak type",
      "laplace-beltrami operator"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1302.0146T"
    }
  }
}