{
  "abstract": "Let $M$ be a complete Riemannian manifold and define a magnetic Schrödinger operator $\\LL = ({\\bf d}+ iA)^*({\\bf d}+iA) + V$ where $A$ is a real $1$-differential form in $L^2_{loc}$ and $V \\in L^1_{loc}$ is a nonnegative electric potential. We prove that the magnetic Riesz transform $({\\bf d} + iA) \\LL^{-\\einhalb}$ is of weak type $(1,1)$ with bound at most $2$. It extends to a bounded operator on $L^p$ for $p \\in (1, 2]$ with norm bounded by a constant $c_p$ depending only on $p$. It is then independent of the dimension of the manifold and independent of $A$ and $V$. We also prove weak type $(1,1)$ bounds for symmetric elliptic operators subject to various boundary conditions on rough domains of $\\RR^d$. The proofs are based on a new weak type $(1,1)$ criterion for operators.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.19469",
  "author_total": 1,
  "authors": [
    {
      "name": "El Maati Ouhabaz"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8myd9t0k45ggp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.19469",
  "fulltext_url": null,
  "id": "8myd9t0k45ggp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.19469",
  "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"
    ],
    [
      "arxiv",
      "math.CA"
    ],
    [
      "arxiv",
      "math.FA"
    ],
    [
      "openalex",
      "2604|Advanced Harmonic Analysis Research"
    ]
  ],
  "openalex": "W7221913662",
  "pdf_url": "https://arxiv.org/pdf/2610.19469",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8myd9t0k45ggp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2610.19469",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.19469"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Weak type $(1,1)$ estimates for Riesz transforms of elliptic operators and magnetic Schrödinger operators",
  "title_text": "Weak type (1,1) estimates for Riesz transforms of elliptic operators and magnetic Schrödinger operators",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/8myd9t0k45ggp",
  "venue": "arXiv",
  "versions": []
}