{
  "id": "math/0612752",
  "version": "v2",
  "published": "2006-12-24T14:03:12.000Z",
  "updated": "2008-06-04T17:03:55.000Z",
  "title": "Restriction of Fourier transforms to curves and related oscillatory integrals",
  "authors": [
    "Jong-Guk Bak",
    "Daniel M. Oberlin",
    "Andreas Seeger"
  ],
  "comment": "Minor changes in the version to appear in American Journal of Mathematics",
  "journal": "American Journal of Mathematics, 131, no.2 (2009), 277-311.",
  "categories": [
    "math.CA"
  ],
  "abstract": "We prove sharp endpoint results for the Fourier restriction operator associated to nondegenerate curves in $\\Bbb R^d$, $d\\ge 3$, and related estimates for oscillatory integral operators. Moreover, for some larger classes of curves in $\\Bbb R^d$ we obtain sharp uniform $L^p\\to L^q$ bounds with respect to affine arclength measure, thereby resolving a problem of Drury and Marshall.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-06-04T17:03:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B99"
    ],
    "keywords": [
      "related oscillatory integrals",
      "fourier transforms",
      "sharp endpoint results",
      "oscillatory integral operators",
      "affine arclength measure"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.....12752B"
    }
  }
}