{
  "id": "1306.4494",
  "version": "v2",
  "published": "2013-06-19T11:29:41.000Z",
  "updated": "2014-05-14T10:57:36.000Z",
  "title": "$L^p$-integrability, dimensions of supports of fourier transforms and applications",
  "authors": [
    "K. S. Senthil Raani"
  ],
  "journal": "Journal of Fourier Analysis and Applications, August 2014, Volume 20, Issue 4, pp 801-815",
  "doi": "10.1007/s00041-014-9334-5",
  "categories": [
    "math.FA"
  ],
  "abstract": "It is proved that there does not exist any non zero function in $L^p(\\R^n)$ with $1\\leq p\\leq 2n/\\alpha$ if its Fourier transform is supported by a set of finite packing $\\alpha$-measure where $0<\\alpha<n$. It is shown that the assertion fails for $p>2n/\\alpha$. The result is applied to prove $L^p$ Wiener-Tauberian theorems for $\\R^n$ and M(2).",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-05-14T10:57:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B10",
      "37F35",
      "40E05",
      "28A78"
    ],
    "keywords": [
      "fourier transform",
      "integrability",
      "applications",
      "dimensions",
      "non zero function"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1306.4494S"
    }
  }
}