{
  "abstract": "In this article, we prove two compactness parabolic extrapolation theorems for linear operators and their commutators on parabolic weighted Lebesgue spaces. As applications, we show that $b\\in\\mathrm{PCMO}$ (parabolic CMO space) if and only if $b\\in L_\\mathrm{loc}^1$ and the commutator $[b,I_α^{γ+}]_k$ is compact from $L^r(ω^r)$ to $L^q(ω^q)$ for any $k\\in\\mathbb{N}$, $1<r<q<\\infty$ with $\\frac{1}{r}-\\frac{1}{q}=α\\in(0,1)$, and $ω\\in A_{r,q}^+(γ)$ (parabolic Muckenhoupt class), where $I_α^{γ+}$ is the parabolic fractional integral. Several other equivalent characterizations of the space $\\mathrm{PCMO}$ are also given. Our approach combines the unweighted compactness for mixed commutators, a local lower estimate for $[b,I_α^{γ+}]_k$, and both a quantitative Uchiyama-type description and the equivalence with $\\inf_T\\{\\|[\\cdot,I_α^{γ+}]_k-T\\|_{L^r\\to L^q}^\\frac{1}{k}\\}$ of $\\mathrm{dist}_{\\mathrm{PBMO}}(\\cdot,\\mathrm{PCMO})$, where the infimum is taken over all compact operators $T:L^r\\to L^q$. Finally, we establish two parabolic weighted Fréchet--Kolmogorov compactness criteria, which further induce a parabolic interpolation theorem of compactness.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.05933",
  "author_total": 5,
  "authors": [
    {
      "name": "Mingming Cao"
    },
    {
      "name": "Weiyi Kong"
    },
    {
      "name": "Dachun Yang"
    },
    {
      "name": "Wen Yuan"
    },
    {
      "name": "Chenfeng Zhu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dgn07z46pgc7z.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.05933",
  "fulltext_url": null,
  "id": "dgn07z46pgc7z",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.05933",
  "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.CA"
    ],
    [
      "arxiv",
      "math.FA"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.05933",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dgn07z46pgc7z.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T15:21:00Z",
      "native_id": "2611.05933",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.05933"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Parabolic Extrapolation of Compactness with Applications to Characterizations of the Parabolic CMO Space via Parabolic Fractional Commutators",
  "title_text": "Parabolic Extrapolation of Compactness with Applications to Characterizations of the Parabolic CMO Space via Parabolic Fractional Commutators",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:14Z",
  "url": "https://research.draconitic.com/paper/dgn07z46pgc7z",
  "venue": "arXiv",
  "versions": []
}