{
  "abstract": "We establish a class of sharp higher-order inequalities related to the uncertainty principle. First, by means of the expanding the squares method, we give a concise proof of sharp higher-order Heisenberg uncertainty principles. We provide explicit expressions for the optimal constants and establish the existence of extremal functions. Furthermore, we obtain sharp higher-order Heisenberg uncertainty principles for curl-free vector fields. In particular, when $N=2$, we give an answer to the higher-order version of Open Problem 9 raised by Maz'ya in [Integr. Equ. Oper. Theory (2018) 90:25]. Second, we establish sharp higher-order Heisenberg uncertainty principles that do not involve higher-order tensors. We also prove sharp higher-order Heisenberg uncertainty principles and higher-order hydrogen uncertainty principles for radially symmetric functions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.01561",
  "author_total": 3,
  "authors": [
    {
      "name": "Hongtao Hu"
    },
    {
      "name": "Meiqi Liu"
    },
    {
      "name": "Wenming Zou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/et80thdpn4zee.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.01561",
  "fulltext_url": null,
  "id": "et80thdpn4zee",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.01561",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2610.01561",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/et80thdpn4zee.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:07Z",
      "native_id": "2610.01561",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.01561"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Sharp higher-order uncertainty principles",
  "title_text": "Sharp higher-order uncertainty principles",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/et80thdpn4zee",
  "venue": "arXiv",
  "versions": []
}