{
  "abstract": "In this short note, we establish dimension-free $\\ell^p(\\mathbb Z^d)$ bounds, for all $p\\in(1,\\infty]$, for the discrete Hardy--Littlewood maximal functions associated with cubes in $\\mathbb Z^d$, answering a question that had been open for a while. The key idea is to prove dimension-free bounds for the $\\ell^p(\\mathbb Z^d)$ norms of the differences of the corresponding averages. This follows from an ad hoc interpretation of the associated discrete multipliers as a special continuous family of multipliers to which basic fractional integration and complex interpolation can be applied. The same method also yields an elementary proof of Bourgain's dimension-free $L^p(\\mathbb R^d)$ bounds for the Hardy--Littlewood maximal function associated with cubes in $\\mathbb R^d$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.24030",
  "author_total": 3,
  "authors": [
    {
      "name": "Mariusz Mirek"
    },
    {
      "name": "Tomasz Z. Szarek"
    },
    {
      "name": "Błażej Wróbel"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2vrfdxmpf1gc7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.24030",
  "fulltext_url": null,
  "id": "2vrfdxmpf1gc7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.24030",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CA"
    ],
    [
      "openalex",
      "2604|Advanced Harmonic Analysis Research"
    ]
  ],
  "openalex": "W7214019368",
  "pdf_url": "https://arxiv.org/pdf/2609.24030",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2vrfdxmpf1gc7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.24030",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.24030"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Dimension-free estimates for discrete maximal functions over cubes in $\\mathbb Z^d$",
  "title_text": "Dimension-free estimates for discrete maximal functions over cubes in ℤ^d",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/2vrfdxmpf1gc7",
  "venue": "arXiv",
  "versions": []
}