{
  "abstract": "We provide kernel estimates for pseudo-differential operators in the $S(m,g)$ Weyl-Hörmander calculus classes. These new results lead to boundedness theorems like the weak (1,1) type for these classes and the boundedness of these operators from Hardy spaces to Lebesgue spaces $L^p$. We prove that under a suitable hypoelliticity condition on the weigh $m,$ one can get the weak (1,1) inequality for the Fefferman order established previously by the second author in analogy to the classical $L^p$-boundedness theorem due to Fefferman. Our approach makes an extension to $S(m,g)$ classes of previous estimates proved by Álvarez and Hounie, Nagase, Kumano-Go, etc, for the Hörmander classes including new regularity properties in this framework from the Hardy space $H^p$ to $L^p$ and also on Lorentz spaces. We have identified that the {\\it Uniform Hörmander Condition} plays a fundamental role in some of our boundedness theorems.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.21692",
  "author_total": 3,
  "authors": [
    {
      "name": "Duván Cardona"
    },
    {
      "name": "Julio Delgado"
    },
    {
      "name": "Manuel Martínez-Flores"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5d6czk85edzyv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.21692",
  "fulltext_url": null,
  "id": "5d6czk85edzyv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.21692",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "openalex",
      "2604|Advanced Harmonic Analysis Research"
    ]
  ],
  "openalex": "W7213878031",
  "pdf_url": "https://arxiv.org/pdf/2609.21692",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5d6czk85edzyv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:07Z",
      "native_id": "2609.21692",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.21692"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Kernel estimates for the Weyl-Hörmander calculus, Weak (1,1) boundedness and other regularity properties",
  "title_text": "Kernel estimates for the Weyl-Hörmander calculus, Weak (1,1) boundedness and other regularity properties",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:07Z",
  "url": "https://research.draconitic.com/paper/5d6czk85edzyv",
  "venue": "arXiv",
  "versions": []
}