{
  "abstract": "In this article, we introduce two bilinear, non-regular symbol classes\\linebreak $BS\\mathcal B^m_δ(r,μ,v;N,λ)$ and $BS\\mathcal F^m_δ(r,μ,v;N,λ)$, where $m\\in\\mathbb R$, $0\\leqδ<1$, $0<μ,v\\leq\\infty$, $1\\leqλ\\leq2$, $r>n/μ$, and $N>2n/λ$, with $μ<\\infty$ for the latter class. For $μ\\geq1$, $(1-δ)r\\geq n/μ$, and sufficiently large $N$, we establish boundedness of the associated bilinear pseudodifferential operators on Besov and Triebel--Lizorkin spaces with variable smoothness, integrability and summation exponents. To the best of the authors' knowledge, these operator estimates are new even on the classical Besov and Triebel--Lizorkin spaces with constant exponents. As an application, we establish the multiplication algebra property for both variable exponent spaces.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.25234",
  "author_total": 3,
  "authors": [
    {
      "name": "Tengfei Bai"
    },
    {
      "name": "Jingshi Xu"
    },
    {
      "name": "Jinlai Zhu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dkqrfsbmjw5fn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.25234",
  "fulltext_url": null,
  "id": "dkqrfsbmjw5fn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.25234",
  "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"
    ],
    [
      "arxiv",
      "math.FA"
    ],
    [
      "openalex",
      "2604|Advanced Harmonic Analysis Research"
    ]
  ],
  "openalex": "W7223054666",
  "pdf_url": "https://arxiv.org/pdf/2610.25234",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dkqrfsbmjw5fn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.25234",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.25234"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Boundedness of nonregular bilinear pseudodifferential operators on variable Besov and Triebel--Lizorkin spaces",
  "title_text": "Boundedness of nonregular bilinear pseudodifferential operators on variable Besov and Triebel--Lizorkin spaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/dkqrfsbmjw5fn",
  "venue": "arXiv",
  "versions": []
}