{
  "abstract": "We establish a weighted restriction estimate in $\\mathbb{R}^2$. Our proof combines new two-ends Furstenberg estimates with refined decoupling.As an application, our result yields decay estimates for the circular $L^p$-means of the Fourier transforms of fractal measures in $\\mathbb{R}^2$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.12587",
  "author_total": 4,
  "authors": [
    {
      "name": "Zhenbin Cao"
    },
    {
      "name": "Feilong Guo"
    },
    {
      "name": "Junfeng Li"
    },
    {
      "name": "Xiangyu Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dmcpzg3vrg79g.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.12587",
  "fulltext_url": null,
  "id": "dmcpzg3vrg79g",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.12587",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CA"
    ],
    [
      "openalex",
      "2604|Advanced Harmonic Analysis Research"
    ]
  ],
  "openalex": "W7212472085",
  "pdf_url": "https://arxiv.org/pdf/2609.12587",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dmcpzg3vrg79g.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2609.12587",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.12587"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "A weighted restriction estimate in $\\mathbb R^2$",
  "title_text": "A weighted restriction estimate in ℝ^2",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/dmcpzg3vrg79g",
  "venue": "arXiv",
  "versions": []
}