{
  "abstract": "We prove several variants of the Brascamp--Lieb inequality which are adapted to additional symmetries, weights, and non-Euclidean radial structures. First, an improved Brascamp--Lieb inequality for even functions yields a strengthened Prékopa--Leindler theorem for even strongly log-concave functions. We also record a Legendre-transform proof of a generalized log-Sobolev inequality for log-concave functions. Further results include a Brascamp--Lieb inequality with a concave weight, an unconditional second-order Poincaré inequality, a rotation-trick improvement for arbitrary even log-concave measures, and a Poincaré-type inequality associated with smooth norms.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.34289",
  "author_total": 3,
  "authors": [
    {
      "name": "Dario Cordero-Erausquin"
    },
    {
      "name": "Galyna V. Livshyts"
    },
    {
      "name": "Liran Rotem"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2dzc9g7s81zte.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.34289",
  "fulltext_url": null,
  "id": "2dzc9g7s81zte",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.34289",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.FA"
    ],
    [
      "arxiv",
      "math.MG"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2604|Mathematical Inequalities and Applications"
    ]
  ],
  "openalex": "W7223799150",
  "pdf_url": "https://arxiv.org/pdf/2610.34289",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2dzc9g7s81zte.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.34289",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.34289"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.MG",
      "subfield": "geometry-topology"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Remarks on the Brascamp--Lieb inequality",
  "title_text": "Remarks on the Brascamp--Lieb inequality",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/2dzc9g7s81zte",
  "venue": "arXiv",
  "versions": []
}