{
  "id": "2109.09691",
  "version": "v1",
  "published": "2021-09-20T17:01:33.000Z",
  "updated": "2021-09-20T17:01:33.000Z",
  "title": "Continuity for the one-dimensional centered Hardy-Littlewood maximal operator at the derivative level",
  "authors": [
    "Cristian González-Riquelme"
  ],
  "comment": "10 pages. 2 figures",
  "categories": [
    "math.CA"
  ],
  "abstract": "We prove the continuity of the map $f \\mapsto (Mf)'$ from $W^{1,1}(\\mathbb{R})$ to $L^1(\\mathbb{R})$, where $M$ is the centered Hardy-Littlewood maximal operator. This solves a question posed by Carneiro, Madrid and Pierce.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-09-20T17:01:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B25",
      "46E35"
    ],
    "keywords": [
      "one-dimensional centered hardy-littlewood maximal operator",
      "derivative level",
      "continuity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}