{
  "id": "2304.12960",
  "version": "v1",
  "published": "2023-04-25T16:09:49.000Z",
  "updated": "2023-04-25T16:09:49.000Z",
  "title": "Restriction type estimates and spectral multipliers on Métivier groups",
  "authors": [
    "Lars Niedorf"
  ],
  "comment": "51 pages",
  "categories": [
    "math.AP",
    "math.FA"
  ],
  "abstract": "We prove a restriction type estimate for sub-Laplacians on arbitrary two-step stratified Lie groups. Despite being slightly weaker than previously known estimates for the subclass of Heisenberg type groups, these estimates surprisingly turn out to be sufficient to prove an $L^p$-spectral multiplier theorem with sharp regularity condition $s>d\\left(1/p-1/2\\right)$ for sub-Laplacians on M\\'etivier groups, up to some exceptional class in dimension $d=15$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-04-25T16:09:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B15",
      "22E25",
      "22E30",
      "43A85"
    ],
    "keywords": [
      "restriction type estimate",
      "métivier groups",
      "arbitrary two-step stratified lie groups",
      "heisenberg type groups",
      "spectral multiplier theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 51,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}