{
  "abstract": "For any \\(n\\geq 1\\), let \\((M,θ)\\) be a compact strictly pseudoconvex hypersurface type CR manifold with dimension \\(2n+1\\), \\(Q=2n+2\\) be its homogeneous dimension. We prove the sharp Folland--Stein Sobolev inequality on \\(M\\): if \\(Q^*=2Q/(Q-2)\\), then there exists a constant \\(A>0\\), depending only on \\((M,θ)\\), such that \\[ \\|u\\|_{L^{Q^*}(M)}^2 \\le K(n)^2\\|\\nabla_b u\\|_{L^2(M)}^2 + A\\|u\\|_{L^2(M)}^2, \\qquad u\\in S^{1,2}(M). \\] Here \\(K(n)\\) is the sharp constant in the Folland--Stein Sobolev inequality on the Heisenberg group \\(\\mathbb H^n\\).",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.09841",
  "author_total": 2,
  "authors": [
    {
      "name": "Zhongwei Tang"
    },
    {
      "name": "Bingwei Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ej8cqnq71mvdd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.09841",
  "fulltext_url": null,
  "id": "ej8cqnq71mvdd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.09841",
  "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.AP"
    ],
    [
      "openalex",
      "2604|Advanced Harmonic Analysis Research"
    ]
  ],
  "openalex": "W7212116263",
  "pdf_url": "https://arxiv.org/pdf/2609.09841",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ej8cqnq71mvdd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:30Z",
      "native_id": "2609.09841",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.09841"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "A Sharp Sobolev Inequality on Compact CR Manifolds",
  "title_text": "A Sharp Sobolev Inequality on Compact CR Manifolds",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:51Z",
  "url": "https://research.draconitic.com/paper/ej8cqnq71mvdd",
  "venue": "arXiv",
  "versions": []
}