{
  "abstract": "We develop a unified multi-scale framework for sparse domination of multilinear operators beyond the multilinear Calderón--Zygmund theory. More precisely, under mild hypotheses on a support condition, weak type and restricted strong type uniform bounds for finite partial sums, and single-scale improving and regularity estimates, we establish $(r_1, \\ldots, r_m, s')$-sparse form bound for a family of localized $m$-linear operators uniformly over all finite partial sums. This sparse bound yields weighted norm inequalities for the corresponding multilinear Muckenhoupt classes $A_{\\vec{p}, (\\vec{r}, s)}$, including the quasi-Banach range. As applications, we determine the optimal open sparse range for multilinear rough singular integrals, and characterize sparse domination for bilinear pseudo-differential operators. Further applications include sparse bounds for bilinear oscillatory Fourier multipliers, bilinear spherical maximal operators, and bilinear Bochner--Riesz means.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.16088",
  "author_total": 3,
  "authors": [
    {
      "name": "Mingming Cao"
    },
    {
      "name": "Binyu Du"
    },
    {
      "name": "Kôzô Yabuta"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4mk14jd3fajrb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.16088",
  "fulltext_url": null,
  "id": "4mk14jd3fajrb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.16088",
  "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.CA"
    ],
    [
      "openalex",
      "2604|Advanced Harmonic Analysis Research"
    ]
  ],
  "openalex": "W7221771379",
  "pdf_url": "https://arxiv.org/pdf/2610.16088",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4mk14jd3fajrb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.16088",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.16088"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Multi-scale analysis for multilinear operators",
  "title_text": "Multi-scale analysis for multilinear operators",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/4mk14jd3fajrb",
  "venue": "arXiv",
  "versions": []
}