{
  "abstract": "We study the Møller wave operators for scaling critical electromagnetic Hamiltonians in the plane. For smooth transverse magnetic and angular electric potentials, with nonnegative angular operator and magnetic flux outside $\\frac12\\Z$, we prove that the wave operators relative to $-Δ$ exist, are unitary on $L^2$, and, together with their adjoints, are bounded on every $L^p$, $1<p<\\infty$. We then specialize to the the Aharonov--Bohm model and we determine the exact ranges for the boundedness of their wave operators on weighted $L^p(\\R^2,|x|^β\\,dx)$ spaces, for both the Friedrichs and the Krein realizations. In the Friedrichs case, this gives in particular the already known boundedness on all $L^{p}$ spaces $1<p<\\infty$, while boundedness fails at $p=1,\\infty$. In the Krein case, both wave operators and adjoints are bounded precisely when $2/(2-η_α)<p<2/η_α$, where $η_α=\\max\\{α,1-α\\}$ (here $α\\in(0,1)$). Thus the boundary condition changes the admissible exponents.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.07464",
  "author_total": 3,
  "authors": [
    {
      "name": "Piero D'Ancona"
    },
    {
      "name": "Xitao Gao"
    },
    {
      "name": "Junyong Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6bf88etq2cnyd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.07464",
  "fulltext_url": null,
  "id": "6bf88etq2cnyd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.07464",
  "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.SP"
    ],
    [
      "openalex",
      "2610|Spectral Theory in Mathematical Physics"
    ]
  ],
  "openalex": "W7212070244",
  "pdf_url": "https://arxiv.org/pdf/2609.07464",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6bf88etq2cnyd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.07464",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.07464"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.SP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "$L^p$ bounds for wave operators with critical electromagnetic potentials",
  "title_text": "L^p bounds for wave operators with critical electromagnetic potentials",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/6bf88etq2cnyd",
  "venue": "arXiv",
  "versions": []
}