{
  "id": "1908.08425",
  "version": "v1",
  "published": "2019-08-22T15:02:45.000Z",
  "updated": "2019-08-22T15:02:45.000Z",
  "title": "Lower bounds for the centered Hardy-Littlewood maximal operator on the real line",
  "authors": [
    "F. J. Pérez Lázaro"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "Let $1<p<\\infty$. We prove that there exists an $\\varepsilon_p>0$ such that for each $f\\in L^p(\\mathbb{R})$, the centered Hardy-Littlewood maximal operator $M$ on $\\mathbb{R}$ satisfies the lower bound $\\|Mf\\|_{L^p(\\mathbb{R})}\\ge (1+\\varepsilon_p)\\|f\\|_{L^p(\\mathbb{R})}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-08-22T15:02:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B25"
    ],
    "keywords": [
      "centered hardy-littlewood maximal operator",
      "lower bound",
      "real line"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}