{
  "abstract": "For the bilinear spherical averages in dimension $d\\geq2$, we show that the lacunary maximal operator is not bounded from $L^1(\\mathbb R^d)\\times L^q(\\mathbb R^d)$ to $L^r(\\mathbb R^d)$ whenever $1\\leq q\\leq\\infty$ and $1/r=1+1/q$. The obstruction is realized by fixed nonnegative inputs; a second construction proves quantitative failure on smooth compactly supported functions and finitely many dyadic scales. The same conclusions hold for the full maximal operator. We give a sharp Lorentz-index criterion in the range $q>d/(d-1)$ and extend the negative result to all multilinear spherical maximal operators with an $L^1$ input. We indicate the precise strong-type boundary statements to which these conclusions apply, without drawing conclusions about separate weak-type or interior estimates.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.14201",
  "author_total": 1,
  "authors": [
    {
      "name": "Vicente Vergara"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fgcse730xdwh9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.14201",
  "fulltext_url": null,
  "id": "fgcse730xdwh9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.14201",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CA"
    ],
    [
      "arxiv",
      "math.FA"
    ],
    [
      "openalex",
      "2604|Advanced Harmonic Analysis Research"
    ]
  ],
  "openalex": "W7221775060",
  "pdf_url": "https://arxiv.org/pdf/2610.14201",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fgcse730xdwh9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.14201",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.14201"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Strong-type endpoint obstructions for bilinear spherical maximal operators",
  "title_text": "Strong-type endpoint obstructions for bilinear spherical maximal operators",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/fgcse730xdwh9",
  "venue": "arXiv",
  "versions": []
}