{
  "id": "1901.06825",
  "version": "v1",
  "published": "2019-01-21T08:47:02.000Z",
  "updated": "2019-01-21T08:47:02.000Z",
  "title": "Boundedness of pseudo-differential operators in subelliptic Sobolev and Besov spaces on compact Lie groups",
  "authors": [
    "Duván Cardona",
    "Michael Ruzhansky"
  ],
  "comment": "29 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "In this paper we investigate the Besov spaces on compact Lie groups in a subelliptic setting, that is, associated with a family of vector fields, satisfying the H\\\"ormander condition, and their corresponding sub-Laplacian. Embedding properties between subelliptic Besov spaces and Besov spaces associated to the Laplacian on the group are proved. We link the description of subelliptic Sobolev spaces with the matrix-valued quantisation procedure of pseudo-differential operators in order to provide subelliptic Sobolev and Besov estimates for operators in the H\\\"ormander classes. Interpolation properties between Besov spaces and Triebel-Lizorkin spaces are also investigated.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-01-21T08:47:02.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "compact lie groups",
      "pseudo-differential operators",
      "boundedness",
      "subelliptic sobolev spaces",
      "subelliptic besov spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}