{
  "id": "math/0409017",
  "version": "v1",
  "published": "2004-09-01T14:28:05.000Z",
  "updated": "2004-09-01T14:28:05.000Z",
  "title": "Characterization of rearrangement invariant spaces with fixed points for the Hardy-Littlewood maximal operator",
  "authors": [
    "Joaquim Martin",
    "Javier Soria"
  ],
  "comment": "8 pages",
  "categories": [
    "math.CA",
    "math.FA"
  ],
  "abstract": "We characterize the rearrangement invariant spaces for which there exists a non-constant fixed point, for the Hardy-Littlewood maximal operator (the case for the spaces $L^p(\\mathbb{R}^{n})$ was first considered by Korry in \\cite{Ko}). The main result that we prove is that the space $L^{\\frac{n}{n-2},\\infty}(\\mathbb{R}^{n})\\cap L^{\\infty}(\\mathbb{R}^{n})$ is minimal among those having this property",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-09-01T14:28:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B25",
      "46E30"
    ],
    "keywords": [
      "rearrangement invariant spaces",
      "hardy-littlewood maximal operator",
      "characterization",
      "non-constant fixed point",
      "main result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......9017M"
    }
  }
}