{
  "abstract": "We prove the sharp Hausdorff--Young inequality on the quantum Euclidean space. Our result implies the sharp Hausdorff--Young constants for the Weyl transform, as well as that for Heisenberg groups. The key ingredient is a novel flow related to the mixed-norm of noncommutative Gabor transform. This, meanwhile, implies a new proof of the classical sharp Hausdorff--Young inequality. We then apply the sharp Hausdorff--Young inequality to establish the sharp Young inequality for noncommutative convolution in the range $1\\le p,q\\le2\\le r\\le\\infty$, with $1/p+1/q=1+1/r$. After appropriate rescaling and trace normalization, this convolution coincides with beam-splitter convolution for bosonic systems, yielding the corresponding Young inequalities with optimal constants in the same range.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.10424",
  "author_total": 2,
  "authors": [
    {
      "name": "Hongsen Qiu"
    },
    {
      "name": "Xiao Xiong"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/05ch5a6aa7mkt.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.10424",
  "fulltext_url": null,
  "id": "05ch5a6aa7mkt",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.10424",
  "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.OA"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "2604|Mathematical Analysis and Transform Methods"
    ]
  ],
  "openalex": "W7212182999",
  "pdf_url": "https://arxiv.org/pdf/2609.10424",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/05ch5a6aa7mkt.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:11Z",
      "native_id": "2609.10424",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.10424"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Noncommutative sharp Hausdorff-Young inequality",
  "title_text": "Noncommutative sharp Hausdorff-Young inequality",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:01Z",
  "url": "https://research.draconitic.com/paper/05ch5a6aa7mkt",
  "venue": "arXiv",
  "versions": []
}