{
  "id": "1111.6409",
  "version": "v2",
  "published": "2011-11-28T11:19:26.000Z",
  "updated": "2013-03-29T08:09:20.000Z",
  "title": "Restriction of Fourier transforms to some complex curves",
  "authors": [
    "Jong-Guk Bak",
    "Seheon Ham"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "The purpose of this paper is to prove a Fourier restriction estimate for certain 2-dimensional surfaces in $\\bbR^{2d}$, $d\\ge 3$. These surfaces are defined by a complex curve $\\gamma(z)$ of simple type, which is given by a mapping of the form % \\[ z\\mapsto \\gamma (z) = \\big(z, \\, z^2,..., \\, z^{d-1}, \\, \\phi(z) \\big) \\] % where $\\phi(z)$ is an analytic function on a domain $\\Omega \\subset \\bbC$. This is regarded as a real mapping $z=(x,y) \\mapsto \\gamma(x,y)$ from $\\Omega \\subset \\bbR^2$ to $\\bbR^{2d}$. Our results cover the case $\\phi(z) = z^N$ for any nonnegative integer $N$, in all dimensions $d\\ge 3$. Furthermore, when $d=3$, we have a uniform estimate, where $\\phi(z)$ may be taken to be an arbitrary polynomial of degree at most $N$. These results are analogues of the uniform restricted strong type estimate in \\cite{BOS3}, valid for polynomial curves of simple type and some other classes of curves in $\\bbR^d$, $d\\ge 3$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-03-29T08:09:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B10",
      "42B99"
    ],
    "keywords": [
      "complex curve",
      "fourier transforms",
      "uniform restricted strong type estimate",
      "simple type",
      "fourier restriction estimate"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1111.6409B"
    }
  }
}