{
  "id": "1411.6950",
  "version": "v1",
  "published": "2014-11-25T18:17:54.000Z",
  "updated": "2014-11-25T18:17:54.000Z",
  "title": "Fourier multipliers on graded Lie groups",
  "authors": [
    "Veronique Fischer",
    "Michael Ruzhansky"
  ],
  "comment": "28 pages",
  "categories": [
    "math.FA",
    "math.RT"
  ],
  "abstract": "We study the $L^p$-boundedness of Fourier multipliers defined on graded nilpotent Lie groups via their group Fourier transform. We show that H\\\"ormander type conditions on the Fourier multipliers imply $L^p$-boundedness. We express these conditions using difference operators and positive Rockland operators. We also obtain a more refined condition using Sobolev spaces on the dual of the group which are defined and studied in this paper.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-11-25T18:17:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "43A22",
      "43A15",
      "22E30"
    ],
    "keywords": [
      "fourier multipliers",
      "graded lie groups",
      "graded nilpotent lie groups",
      "group fourier transform",
      "sobolev spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1411.6950F"
    }
  }
}