{
  "id": "math/0608129",
  "version": "v2",
  "published": "2006-08-04T18:42:32.000Z",
  "updated": "2006-09-21T22:40:11.000Z",
  "title": "The Fourier extension operator on large spheres and related oscillatory integrals",
  "authors": [
    "Jonathan Bennett",
    "Andreas Seeger"
  ],
  "journal": "Proceedings of the London Mathematical Society, 98, no.1, (2009), 45-82.",
  "doi": "10.1112/plms/pdn022",
  "categories": [
    "math.CA"
  ],
  "abstract": "We obtain new estimates for a class of oscillatory integral operators with folding canonical relations satisfying a curvature condition. The main lower bounds showing sharpness are proved using Kakeya set constructions. As a special case of the upper bounds we deduce optimal $L^p(mathbb{S}^2)\\to L^q(R \\mathbb{S}^2)$ estimates for the Fourier extension operator on large spheres in $\\mathbb{R}^3$, which are uniform in the radius $R$. Two appendices are included, one concerning an application to Lorentz space bounds for averaging operators along curves in $R^3$, and one on bilinear estimates.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2006-09-21T22:40:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B99",
      "35S30"
    ],
    "keywords": [
      "fourier extension operator",
      "related oscillatory integrals",
      "large spheres",
      "main lower bounds showing sharpness",
      "kakeya set constructions"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}