{
  "abstract": "We extend the Bourgain--Brézis--Mironescu (BBM) and Maz'ya--Shaposhnikova (MS) limit formulae to higher-order Besov norms on quantum Euclidean spaces $\\R^d_θ$, a fundamental class of noncompact noncommutative manifolds obtained by deformation quantization of $\\R^d$. A central ingredient is a Banach realization of the homogeneous Sobolev endpoint that forms a compatible couple with \\(L_p(\\R_θ^d)\\), together with the equivalence \\[ K\\bigl(\\x,\\varepsilon^k; L_p(\\R_θ^d),\\dot W_{p,0}^k(\\R_θ^d)\\bigr) \\approx ω_p^k(\\x,\\varepsilon). \\] This framework yields a unified proof of both endpoint formulae through the endpoint continuity of real interpolation scales. The principal new ingredient at the MS endpoint is the sharp large-translation asymptotic \\[ \\lim_{|h|\\to\\infty}\\|T_h\\x-\\x\\|_p = 2^{1/p}\\|\\x\\|_p, \\qquad \\x\\in L_p(\\R_θ^d),\\quad 1\\leq p<\\infty, \\] whose proof combines oscillatory decay of the non-pure terms in the tracial expansion with weighted spectral-measure arguments adapted to the semifinite trace.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.26463",
  "author_total": 4,
  "authors": [
    {
      "name": "Qingquan Deng"
    },
    {
      "name": "Guixiang Hong"
    },
    {
      "name": "Ping Li"
    },
    {
      "name": "Yanzhen Long"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1mtpz8d3rsa2n.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.26463",
  "fulltext_url": null,
  "id": "1mtpz8d3rsa2n",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.26463",
  "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.CA"
    ],
    [
      "arxiv",
      "math.FA"
    ],
    [
      "openalex",
      "2610|Advanced Operator Algebra Research"
    ]
  ],
  "openalex": "W7223056650",
  "pdf_url": "https://arxiv.org/pdf/2610.26463",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1mtpz8d3rsa2n.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.26463",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.26463"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Limits of Besov Norms on Quantum Euclidean Spaces",
  "title_text": "Limits of Besov Norms on Quantum Euclidean Spaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/1mtpz8d3rsa2n",
  "venue": "arXiv",
  "versions": []
}