{
  "id": "2010.15024",
  "version": "v1",
  "published": "2020-10-28T14:59:33.000Z",
  "updated": "2020-10-28T14:59:33.000Z",
  "title": "A note on decreasing rearrangement and mean oscillation on measure spaces",
  "authors": [
    "Almut Burchard",
    "Galia Dafni",
    "Ryan Gibara"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "We derive bounds on the mean oscillation of the decreasing rearrangement $f^*$ on $\\mathbb{R}_+$ in terms of the mean oscillation of $f$ on a suitable measure space $X$. In the special case of a doubling metric measure space, the bound depends only on the doubling constant.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-10-28T14:59:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "30L15",
      "42B35",
      "46E30"
    ],
    "keywords": [
      "mean oscillation",
      "decreasing rearrangement",
      "doubling metric measure space",
      "suitable measure space",
      "special case"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}