{
  "abstract": "We prove the sharp $\\ell^p$ bound $p^\\star-1$ for certain second-order discrete Riesz transforms on products of integers, in all dimensions. The family includes the imaginary part of the discrete Beurling-Ahlfors operator in dimension two as a special case. While these operators admit a martingale representation via compound Poisson jump processes and heat extensions, the martingale attached to a function and the martingale attached to its transform do not enjoy strong differential subordination, so the operator-norm estimate is not accessible through prior work.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.13573",
  "author_total": 2,
  "authors": [
    {
      "name": "Komla Domelevo"
    },
    {
      "name": "Stefanie Petermichl"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dvxqpxbkp57m9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.13573",
  "fulltext_url": null,
  "id": "dvxqpxbkp57m9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.13573",
  "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.PR"
    ],
    [
      "openalex",
      "2604|Advanced Harmonic Analysis Research"
    ]
  ],
  "openalex": "W7213369961",
  "pdf_url": "https://arxiv.org/pdf/2609.13573",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dvxqpxbkp57m9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:45Z",
      "native_id": "2609.13573",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.13573"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "The sharp $L^p$ bound for the imaginary part of the Beurling-Ahlfors operator on the lattice",
  "title_text": "The sharp L^p bound for the imaginary part of the Beurling-Ahlfors operator on the lattice",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:45Z",
  "url": "https://research.draconitic.com/paper/dvxqpxbkp57m9",
  "venue": "arXiv",
  "versions": []
}