{
  "abstract": "We determine the optimal constant in the $L^p$-derivative inequality for the uncentered Hardy--Littlewood maximal operator on the real line for every $1<p<\\infty$. It is the unique number $γ_p\\in [0,1]$ satisfying $(2p-1)γ_p+(p-1)γ_p^{(2p-1)/(p-1)}=p$. As $p$ goes from $1$ to $+\\infty$, $γ_p$ decreases from $1$ to $\\sqrt2-1$, and at the endpoints the limiting arguments recover the classical total-variation and Lipschitz inequalities, with the qualitative regularity ingredient at the $BV$ endpoint supplied by Aldaz and Pérez Lázaro.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.39178",
  "author_total": 3,
  "authors": [
    {
      "name": "Sung-Yi Liao"
    },
    {
      "name": "José Madrid"
    },
    {
      "name": "Eyvindur Ari Palsson"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0jt2hcr13cz50.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.39178",
  "fulltext_url": null,
  "id": "0jt2hcr13cz50",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.39178",
  "language": null,
  "licence": "CC-BY-SA-4.0",
  "licence_label": "CC BY-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CA"
    ],
    [
      "arxiv",
      "math.FA"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.39178",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0jt2hcr13cz50.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.39178",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.39178"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Sharp derivative inequalities for maximal functions",
  "title_text": "Sharp derivative inequalities for maximal functions",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/0jt2hcr13cz50",
  "venue": "arXiv",
  "versions": []
}