{
  "abstract": "We prove the existence of a bounded Sobolev extension operator $E:W^{p,1}\\left( B,P \\right) \\rightarrow W^{p,1}\\left( \\ell^{2} ,P \\right)$ using a completely new method, where $B\\subset \\ell^{2}$ is the unit ball and $P$ is any non-trivial centered Gaussian measure on $\\ell^{2}$. This solves an open problem posed in the literatures.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.06229",
  "author_total": 3,
  "authors": [
    {
      "name": "Zhouzhe Wang"
    },
    {
      "name": "Xu Zhang"
    },
    {
      "name": "Shiliang Zhao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dscr3fdq19r28.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.06229",
  "fulltext_url": null,
  "id": "dscr3fdq19r28",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.06229",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.FA"
    ],
    [
      "openalex",
      "2610|Advanced Banach Space Theory"
    ]
  ],
  "openalex": "W7163705637",
  "pdf_url": "https://arxiv.org/pdf/2606.06229",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dscr3fdq19r28.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:40Z",
      "native_id": "2606.06229",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.06229"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Extension of Sobolev functions on balls in infinite dimensions",
  "title_text": "Extension of Sobolev functions on balls in infinite dimensions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:40Z",
  "url": "https://research.draconitic.com/paper/dscr3fdq19r28",
  "venue": "arXiv",
  "versions": []
}