{
  "abstract": "We solve the kinetic Kato square root problem for the whole-space Kolmogorov operator $$H_A=\\partial_t-X\\cdot\\nabla_Y-\\operatorname{div}_X(A\\nabla_X)$$ on \\(\\mathrm L^2\\) with Lebesgue measure, where \\(A\\) is a bounded measurable complex uniformly accretive matrix depending on all variables. We define its realization through a sesquilinear form and identify the square-root domains of the resulting maximal accretive operator and its adjoint with the intrinsic Sobolev space defined by one velocity derivative and half a derivative along the transport flow. The homogeneous norm equivalences depend only on the dimension and the coefficient bounds. The energy also controls a position derivative of order one third. The proof uses second-order resolvents and localized affine testing. A regularized transport symmetrizer gives hidden coercivity, while comparison with a positive Rockland operator supplies intrinsic smoothing. Commutator and dyadic approximation estimates remove the smoothing before a Carleson argument is applied. We also obtain uniform shifted square-root estimates and bounded velocity, transport and position Riesz transforms.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.03104",
  "author_total": 1,
  "authors": [
    {
      "name": "Kaj Nyström"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cd94s8d7y68vs.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.03104",
  "fulltext_url": null,
  "id": "cd94s8d7y68vs",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.03104",
  "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"
    ],
    [
      "arxiv",
      "math.FA"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.03104",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cd94s8d7y68vs.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:14Z",
      "native_id": "2611.03104",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.03104"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "The kinetic Kato square root problem",
  "title_text": "The kinetic Kato square root problem",
  "type": "preprint",
  "updated_at": "2026-11-04T15:21:12Z",
  "url": "https://research.draconitic.com/paper/cd94s8d7y68vs",
  "venue": "arXiv",
  "versions": []
}