{
  "abstract": "We prove a continuous-time Carleson embedding theorem with constant $e$ for a system of square-integrable continuous martingales whose quadratic covariations mimic the generalised Cauchy--Riemann relations. The argument is based on a Bellman function and a multidimensional Itô formula. As an application we transfer the estimate to the upper half-space via the Gundy--Varopoulos representation and obtain a Carleson embedding, still with constant $e$, for the vector consisting of a function and its Riesz transforms in arbitrary dimension.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.39919",
  "author_total": 5,
  "authors": [
    {
      "name": "Komla Domelevo"
    },
    {
      "name": "Johanna Fladung"
    },
    {
      "name": "Spyridon Kakaroumpas"
    },
    {
      "name": "Paul Montobbio"
    },
    {
      "name": "Stefanie Petermichl"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/49vbbfprv8hh1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.39919",
  "fulltext_url": null,
  "id": "49vbbfprv8hh1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.39919",
  "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.CA"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2604|Advanced Harmonic Analysis Research"
    ]
  ],
  "openalex": "W7215088124",
  "pdf_url": "https://arxiv.org/pdf/2609.39919",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/49vbbfprv8hh1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:49Z",
      "native_id": "2609.39919",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.39919"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "A stochastic Carleson embedding theorem with constant $e$ and the vector of Riesz transforms",
  "title_text": "A stochastic Carleson embedding theorem with constant e and the vector of Riesz transforms",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:49Z",
  "url": "https://research.draconitic.com/paper/49vbbfprv8hh1",
  "venue": "arXiv",
  "versions": []
}