{
  "abstract": "In this paper we prove that if a Wiener functional $F$ is $1+δ$-differentiable in the Malliavin sense for some $δ>0$ and satisfies the nondegeneracy condition, then the density of the law of $F$ exists, is bounded and is Hölder continuous of every exponent $β<δ$. This gives a partial positive answer to a problem proposed by Watanabe [13]; to date, this seems to be the best result available for the boundedness of the density of Wiener functionals. The approach is based on the fractional order Sobolev spaces associated with a probability measure and on the Riesz transform.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.33578",
  "author_total": 1,
  "authors": [
    {
      "name": "Hua Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9cbgbd97jcxg9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.33578",
  "fulltext_url": null,
  "id": "9cbgbd97jcxg9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.33578",
  "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.PR"
    ],
    [
      "openalex",
      "2003|Stochastic processes and financial applications"
    ]
  ],
  "openalex": "W7223912109",
  "pdf_url": "https://arxiv.org/pdf/2610.33578",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9cbgbd97jcxg9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.33578",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.33578"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Boundedness of the Density of Wiener Functionals with Low Regularity",
  "title_text": "Boundedness of the Density of Wiener Functionals with Low Regularity",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/9cbgbd97jcxg9",
  "venue": "arXiv",
  "versions": []
}