{
  "id": "1308.2268",
  "version": "v1",
  "published": "2013-08-10T02:34:14.000Z",
  "updated": "2013-08-10T02:34:14.000Z",
  "title": "Growth and integrability of Fourier transforms on Euclidean space",
  "authors": [
    "William O. Bray"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "A fundamental theme in classical Fourier analysis relates smoothness properties of functions to the growth and/or integrability of their Fourier transform. By using a suitable class of $L^{p}-$multipliers, a rather general inequality controlling the size of Fourier transforms for large and small argument is proved. As consequences, quantitative Riemann-Lebesgue estimates are obtained and an integrability result for the Fourier transform is developed extending ideas used by Titchmarsh in the one dimensional setting.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-08-10T02:34:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B10"
    ],
    "keywords": [
      "fourier transform",
      "euclidean space",
      "integrability",
      "fourier analysis relates smoothness properties",
      "classical fourier analysis relates smoothness"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1308.2268B"
    }
  }
}