{
  "id": "1508.03277",
  "version": "v1",
  "published": "2015-08-13T17:34:18.000Z",
  "updated": "2015-08-13T17:34:18.000Z",
  "title": "A method of rotations for Lévy Multipliers",
  "authors": [
    "Michael Perlmutter"
  ],
  "categories": [
    "math.PR",
    "math.FA"
  ],
  "abstract": "We use a method of rotations to study the $L^p$ boundedness, $1<p<\\infty$, of Fourier multipliers which arise as the projection of martingale transforms with respect to symmetric $\\alpha$-stable processes, $0<\\alpha<2$. Our proof does not use the fact that $0<\\alpha<2$, and therefore allows us to obtain a larger class of multipliers which are bounded on $L^p$. As in the case of the multipliers which arise as the projection of martingale transforms, these new multipliers also have potential applications to the study of the $L^p$ boundedness of the Beurling-Ahlfors transform.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-08-13T17:34:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G46",
      "42A61"
    ],
    "keywords": [
      "lévy multipliers",
      "martingale transforms",
      "projection",
      "boundedness",
      "fourier multipliers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150803277P"
    }
  }
}