{
  "abstract": "Let M be a complete Riemannian manifold satisfying the doubling volume condition for geodesic balls and L^q scaled Poincaré inequalities on suitable remote balls for some q<2. We prove the inequality $||\\Delta^{1/2}f||_p\\lesssim ||\\nabla f||_p$ for all p ∈ (q, 2], which generalizes previous results due to Auscher and Coulhon. Our conclusion applies, in particular, when M has a finite number of Euclidean ends. The proof strongly relies on Hardy inequalities, which are also new in this context and of independent interest.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2209.05083",
  "author_total": 2,
  "authors": [
    {
      "name": "Baptiste Devyver"
    },
    {
      "name": "Emmanuel Russ"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/17grx398wm0je.bib",
  "cited_by": 0,
  "doi": null,
  "fulltext_url": null,
  "id": "17grx398wm0je",
  "issns": [],
  "landing_url": "https://hal.science/hal-03773356v2",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.math"
    ],
    [
      "hal",
      "1.math.math-ap"
    ],
    [
      "hal",
      "1.math.math-ca"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://hal.science/hal-03773356/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/17grx398wm0je.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:58Z",
      "native_id": "hal-03773356",
      "source": "hal",
      "url": "https://hal.science/hal-03773356v2"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-ap",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "REVERSE INEQUALITY FOR THE RIESZ TRANSFORMS ON RIEMANNIAN MANIFOLDS",
  "title_text": "REVERSE INEQUALITY FOR THE RIESZ TRANSFORMS ON RIEMANNIAN MANIFOLDS",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:58Z",
  "url": "https://research.draconitic.com/paper/17grx398wm0je",
  "venue": "HAL",
  "versions": []
}