{
  "abstract": "Let $Γ=\\{1,\\dots,d\\}$, $d\\geq 2$. For each $j\\in Γ$, let ${\\ell}_{j}\\geq 1$ be an integer and let $α_{j}\\in (1/2,1)$. We obtain a pointwise estimate for the integral \\begin{equation*} \\int_{\\mathbb{S}^{d-1}}\\prod_{j\\in Γ} |x^{\\ell_{j}}_{j}-ξ_{j}|^{-α_{j}} d σ(x), \\end{equation*} in the region \\begin{equation*} \\{ξ\\in \\mathbb{R}^{d}: ξ_{j}\\neq 0,\\;j\\inΓ,\\;\\; \\sum\\nolimits_{j\\in F}|ξ_{j}|^{2/\\ell_{j}}\\neq 1,\\; F\\subseteq Γ\\}. \\end{equation*} These estimates are used to prove a Stein-Tomas type restriction theorem for the oscillatory integral operator $Tf(x)=\\int_{\\mathbb{R}^d}e^{\\dot{\\imath}h(x,y)}f(y)dy$, with the phase $h(x,y)=\\sum\\nolimits_{j\\inΓ} a_{j} x_{j}^{\\ell_{j}} y_{j}^{m_{j}}$, where, for each $j\\in Γ$, $a_{j}\\neq 0$ is a real number and $m_{j}>1$ is an integer.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.11942",
  "author_total": 1,
  "authors": [
    {
      "name": "Ahmed A. Abdelhakim"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/60q82bqn6j8wh.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.11942",
  "fulltext_url": null,
  "id": "60q82bqn6j8wh",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.11942",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CA"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.11942",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/60q82bqn6j8wh.ris",
  "sources": [
    {
      "first_seen": "2026-11-10T06:21:34Z",
      "native_id": "2611.11942",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.11942"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Pointwise estimates for an anisotropic product type singular integral on the sphere",
  "title_text": "Pointwise estimates for an anisotropic product type singular integral on the sphere",
  "type": "preprint",
  "updated_at": "2026-11-10T06:21:34Z",
  "url": "https://research.draconitic.com/paper/60q82bqn6j8wh",
  "venue": "arXiv",
  "versions": []
}