{
  "abstract": "We prove dimension-free higher-order Sobolev norm estimates on open convex subsets of $\\mathbb{R}^n$ with respect to Gaussian measure and use them to obtain norm equivalence on nonempty open convex subsets of $\\ell^2$ endowed with a nondegenerate Gaussian measure. To the best of our knowledge, this is the first such equivalence theorem on a proper open subset of an infinite-dimensional Hilbert space, beyond the earlier whole-space results. We also prove the Malliavin--Sobolev norm equivalence for all $p\\in[1,\\infty)$ and $k\\ge2$, including the case $p=1$, $k\\ge3$ left open by Addona--Muratori--Rossi in \\cite{AddonaMuratoriRossi}.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.24702",
  "author_total": 1,
  "authors": [
    {
      "name": "Zhouzhe Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4a4m2hjnafhgy.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.24702",
  "fulltext_url": null,
  "id": "4a4m2hjnafhgy",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.24702",
  "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.FA"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7204500069",
  "pdf_url": "https://arxiv.org/pdf/2608.24702",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4a4m2hjnafhgy.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:40Z",
      "native_id": "2608.24702",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.24702"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "On the equivalence of Sobolev norms in infinite dimensions",
  "title_text": "On the equivalence of Sobolev norms in infinite dimensions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:40Z",
  "url": "https://research.draconitic.com/paper/4a4m2hjnafhgy",
  "venue": "arXiv",
  "versions": []
}