{
  "abstract": "Let $M$ be a complete, non-compact Riemannian manifold. We prove that its Riesz transform is of weak type $(1,1)$, with constant $2$ for real-valued functions. Consequently, it is bounded on $L^p(M)$ for $1<p\\leq2$, with constants depending only on $p$, which proves the Coulhon--Duong conjecture. The proof uses an obstacle decomposition for positive self-adjoint operators with sub-Markovian semigroups. Applying this decomposition to the shifted square-root Laplacian and using locality of the Sobolev differential yields the endpoint estimate without geometric or heat kernel assumptions. We also obtain the corresponding result for Dirichlet spaces admitting a local Hilbertian differential calculus.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.23503",
  "author_total": 4,
  "authors": [
    {
      "name": "Rui Chen"
    },
    {
      "name": "Renjin Jiang"
    },
    {
      "name": "Bo Li"
    },
    {
      "name": "Hong-Quan Li"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fnqr3pv1yzgq5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.23503",
  "fulltext_url": null,
  "id": "fnqr3pv1yzgq5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.23503",
  "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.CA"
    ],
    [
      "arxiv",
      "math.DG"
    ],
    [
      "openalex",
      "2604|Advanced Harmonic Analysis Research"
    ]
  ],
  "openalex": "W7214007750",
  "pdf_url": "https://arxiv.org/pdf/2609.23503",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fnqr3pv1yzgq5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.23503",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.23503"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "The Coulhon--Duong conjecture for the Riesz transform on complete Riemannian manifolds",
  "title_text": "The Coulhon--Duong conjecture for the Riesz transform on complete Riemannian manifolds",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/fnqr3pv1yzgq5",
  "venue": "arXiv",
  "versions": []
}