{
  "abstract": "We prove power-loss results for some variants of Stein's Weighted $L^2$ Conjecture for Bochner-Riesz means. The variants concern multipliers by convex bodies with $C^k$ boundaries in every dimension $n$. The counterexamples are related to recently-constructed counterexamples to the Mizohata-Takeuchi Conjecture. Related results like logarithmic blowups for the endpoint case of the original conjecture are also discussed.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.27045",
  "author_total": 1,
  "authors": [
    {
      "name": "Ruixiang Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c8d15actc3fj4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.27045",
  "fulltext_url": null,
  "id": "c8d15actc3fj4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.27045",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CA"
    ],
    [
      "openalex",
      "2604|Advanced Harmonic Analysis Research"
    ]
  ],
  "openalex": "W7214205086",
  "pdf_url": "https://arxiv.org/pdf/2609.27045",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c8d15actc3fj4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:00Z",
      "native_id": "2609.27045",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.27045"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "On $C^k$ convex variants of Stein's Weighted $L^2$ Conjecture for Bochner-Riesz means",
  "title_text": "On C^k convex variants of Stein's Weighted L^2 Conjecture for Bochner-Riesz means",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/c8d15actc3fj4",
  "venue": "arXiv",
  "versions": []
}