{
  "id": "1807.04399",
  "version": "v1",
  "published": "2018-07-12T02:11:27.000Z",
  "updated": "2018-07-12T02:11:27.000Z",
  "title": "Centered Hardy--Littlewood maximal operator on the real line: lower bounds",
  "authors": [
    "Paata Ivanisvili",
    "Samuel Zbarsky"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "For $1<p<\\infty$ and $M$ the centered Hardy-Littlewood maximal operator on $\\mathbb{R}$, we consider whether there is some $\\varepsilon=\\varepsilon(p)>0$ such that $\\|Mf\\|_p\\ge (1+\\varepsilon)||f||_p$. We prove this for $1<p<2$. For $2\\le p<\\infty$, we prove the inequality for indicator functions and for unimodal functions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-07-12T02:11:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B25"
    ],
    "keywords": [
      "centered hardy-littlewood maximal operator",
      "lower bounds",
      "real line",
      "unimodal functions",
      "indicator functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}