{
  "abstract": "We prove the Trudinger inequality with exponent $\\frac{s}{s-1}$ for $M^{1,s}$ Sobolev spaces on metric measure spaces under the sole measure growth assumption $μ(B(x,r))\\ge br^s$. This improves the previously known exponential integrability with power one. Our argument also yields sharp asymptotic bounds for the Sobolev constants as $p\\uparrow s$. On doubling spaces, we further remove the connectedness assumption from the Trudinger inequality associated with a $(1,p)$-Poincaré inequality when $p<s$. An Ahlfors regular counterexample shows that this extension fails at the critical exponent $p=s$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.09101",
  "author_total": 3,
  "authors": [
    {
      "name": "Ryan Alvarado"
    },
    {
      "name": "Ahmed Dughayshim"
    },
    {
      "name": "Piotr Hajłasz"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/701nsy9ntc19a.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.09101",
  "fulltext_url": null,
  "id": "701nsy9ntc19a",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.09101",
  "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"
    ],
    [
      "arxiv",
      "math.FA"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7212077163",
  "pdf_url": "https://arxiv.org/pdf/2609.09101",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/701nsy9ntc19a.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:01Z",
      "native_id": "2609.09101",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.09101"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "The Trudinger inequality is true for $M^{1,s}$ spaces",
  "title_text": "The Trudinger inequality is true for M^1,s spaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:01Z",
  "url": "https://research.draconitic.com/paper/701nsy9ntc19a",
  "venue": "arXiv",
  "versions": []
}