{
  "abstract": "In this paper, we establish a higher order Morrey's inequality in the framework of $\\mathsf{CD}(K,N)$-spaces for $K\\in\\mathbb{R}$ and $N\\in\\mathbb{N}$. We do so by first introducing an alternate version of second order Sobolev spaces in general metric measure spaces, which contains amply many functions even when $p>N$. These spaces contain the traditional $H^{2, p}(X)$ spaces on $\\mathsf{RCD}(K, N)$-spaces.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.24404",
  "author_total": 2,
  "authors": [
    {
      "name": "Jun Kitagawa"
    },
    {
      "name": "Kazuhiro Kuwae"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5pztz12dm8qk1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.24404",
  "fulltext_url": null,
  "id": "5pztz12dm8qk1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.24404",
  "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.MG"
    ],
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      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7162393685",
  "pdf_url": "https://arxiv.org/pdf/2605.24404",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5pztz12dm8qk1.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T15:21:28Z",
      "native_id": "2605.24404",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.24404"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.MG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "On higher order Morrey's inequalities over CD{\\boldmath$(K,N)$}-spaces",
  "title_text": "On higher order Morrey's inequalities over CD{\\boldmath(K,N)}-spaces",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:01Z",
  "url": "https://research.draconitic.com/paper/5pztz12dm8qk1",
  "venue": "arXiv",
  "versions": []
}