{
  "abstract": "We study semigroups of composition operators acting on the Besov spaces $B_p$, where they exhibit some new behaviors relative to many classical spaces. Often for a Banach space $X$ of analytic functions on the unit disk, the maximal closed space of strong continuity, $[ φ_t, X ]$, exists for every semigroup $\\{ φ_t \\}$ of analytic self-maps of the disk, and the question whether $[φ_t , X ]$ equals $X$ itself has an answer independent of $\\{φ_t\\}$. Such is the case for the Hardy and Bergman spaces, Bloch, BMOA, and $H^{\\infty}$. For the disk algebra $A$, $[φ_t , A ] = A$ precisely when $\\{φ_t\\} \\subset A$. For $B_p$ with $p \\geq 2$, every $\\{φ_t\\} \\subset B_p$ and always $[ φ_t, B_p ] = B_p$, but this fails when $1 < p < 2$. We give an example where $\\{φ_t\\} \\subset B_p$ and yet the induced composition operators $\\{C_t\\}$ are not bounded on $B_p$ and we do not know if $[φ_t,B_p]$ exists. If it does exist, it cannot be equal to $B_p$. Under the hypothesis that there is a uniform bound for the operator norms of the $\\{C_t\\}$, $0 \\leq t \\leq 1$, we characterize the semigroups $\\{ φ_t \\}$ such that $[ φ_t, B_p ] = B_p$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: Complex Analysis and Operator Theory (2025) 19:64",
  "arxiv": "2607.21878",
  "author_total": 3,
  "authors": [
    {
      "name": "Austin Anderson"
    },
    {
      "name": "Mirjana Jovovic"
    },
    {
      "name": "Wayne Smith"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cdwbrb8enk8j6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.21878",
  "fulltext_url": null,
  "id": "cdwbrb8enk8j6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.21878",
  "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.CV"
    ],
    [
      "arxiv",
      "math.FA"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2607.21878",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cdwbrb8enk8j6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:23Z",
      "native_id": "2607.21878",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.21878"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Composition Semigroups on the Besov Spaces",
  "title_text": "Composition Semigroups on the Besov Spaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:23Z",
  "url": "https://research.draconitic.com/paper/cdwbrb8enk8j6",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.1007/s11785-025-01686-7",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}