{
  "abstract": "Regarding the Besov space ${\\rm B}_1^{Φ_2}$, defined by S. Geiss and Ylinen (Memoirs AMS 1335, 2021) by a coupling method, we prove for $ξ\\in{\\rm B}_1^{Φ_2} \\cap L_2$ a distributional estimate in terms of the Lorentz-Zygmund space $L_{1,\\infty}(\\ln L)^{-1}$ for the Malliavin derivative ${\\rm D}(T_uξ)$ uniformly in $u>0$, where $(T_u)_{u\\ge }$ is the Ornstein-Uhlenbeck semi-group. Here $ξ$ is not necessarily Malliavin differentiable in the ${\\rm D}_{1,1}$-sense. This provides for Theorem 4.22 of the aforementioned reference an extension to the borderline case $p=1$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.36152",
  "author_total": 1,
  "authors": [
    {
      "name": "Stefan Geiss"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dpzz5xjcy6nf1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.36152",
  "fulltext_url": null,
  "id": "dpzz5xjcy6nf1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.36152",
  "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.FA"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2604|Advanced Harmonic Analysis Research"
    ]
  ],
  "openalex": "W7224085108",
  "pdf_url": "https://arxiv.org/pdf/2610.36152",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dpzz5xjcy6nf1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:53Z",
      "native_id": "2610.36152",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.36152"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "A note on the Besov spaces ${\\rm B}_1^{Φ_2}$",
  "title_text": "A note on the Besov spaces B_1^Φ_2",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:53Z",
  "url": "https://research.draconitic.com/paper/dpzz5xjcy6nf1",
  "venue": "arXiv",
  "versions": []
}