{
  "abstract": "We consider the Stokes operator $A$ on smooth exterior domains $Ω$ of $\\mathbb{R}^n$ in homogeneous Sobolev spaces $\\widehat H^{κ,q}_w(Ω)$ with radially symmetric Muckenhoupt weights $w\\in \\mathscr A_q$. A fundamental property is the existence of a bounded $\\mathscr H^\\infty$-calculus of the Stokes operator on weighted nonhomogeneous and homogeneous $L^q$ Sobolev spaces. This property implies the existence of uniformly bounded purely imaginary powers $A^{it}$, $t\\in\\mathbb{R}$, and the characterization of domains of fractional powers $A^θ$ equipped with nonhomogeneous ($\\| u\\|_{L^q_w} + \\|A^θu\\|_{L^q_w}$) as well as homogeneous norm ($\\|A^θu\\|_{L^q_w}$) as complex interpolation spaces. The final aim is the identification with homogeneous spaces $\\widehat{\\mathcal D}((-Δ_{q,w})^θ) = [L^q_{w},\\widehat{\\mathcal D}(-Δ_{q,w})]_θ$ intersected by a space of solenoidal vector fields. Moreover, we obtain weighted variational inequalities for weak solutions of the Stokes equations, weighted $L^q$-$L^r$ decay estimates of the Stokes semigroup and $L^p$-maximal regularity on $L^q_{σ,w}(Ω)$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.29002",
  "author_total": 2,
  "authors": [
    {
      "name": "Reinhard Farwig"
    },
    {
      "name": "Kazuyuki Tsuda"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c649yqhejrcx9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.29002",
  "fulltext_url": null,
  "id": "c649yqhejrcx9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.29002",
  "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.AP"
    ],
    [
      "openalex",
      "2604|Advanced Harmonic Analysis Research"
    ]
  ],
  "openalex": "W7204923768",
  "pdf_url": "https://arxiv.org/pdf/2608.29002",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c649yqhejrcx9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:48Z",
      "native_id": "2608.29002",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.29002"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "The Stokes Operator on Exterior Domains in Homogeneous Weighted Function Spaces:From Weak Theory to $\\mathscr H^\\infty$-calculus to Fractional Domains",
  "title_text": "The Stokes Operator on Exterior Domains in Homogeneous Weighted Function Spaces:From Weak Theory to ℋ^∞-calculus to Fractional Domains",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/c649yqhejrcx9",
  "venue": "arXiv",
  "versions": []
}