{
  "id": "1111.7212",
  "version": "v1",
  "published": "2011-11-30T15:39:31.000Z",
  "updated": "2011-11-30T15:39:31.000Z",
  "title": "Martingales and Sharp Bounds for Fourier multipliers",
  "authors": [
    "Rodrigo Bañuelos",
    "Adam O\\cekowski"
  ],
  "categories": [
    "math.PR",
    "math.FA"
  ],
  "abstract": "Using the argument of Geiss, Montgomery-Smith and Saksman \\cite{GMSS}, and a new martingale inequality, the $L^p$--norms of certain Fourier multipliers in $\\R^d$, $d\\geq 2$, are identified. These include, among others, the second order Riesz transforms $R_j^2$, $j=1, 2,..., d$, and some of the L\\'evy multipliers studied in \\cite{BBB}, \\cite{BB}",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-11-30T15:39:31.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fourier multipliers",
      "sharp bounds",
      "second order riesz transforms",
      "levy multipliers",
      "martingale inequality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1111.7212B"
    }
  }
}