{
  "id": "1702.02033",
  "version": "v1",
  "published": "2017-02-07T14:24:20.000Z",
  "updated": "2017-02-07T14:24:20.000Z",
  "title": "Domains of type 1,1 operators: a case for Triebel--Lizorkin spaces",
  "authors": [
    "Jon Johnsen"
  ],
  "comment": "4 pages. Appeared in Comptes Rendu Mathematiques in 2004",
  "journal": "Comptes Rendus Academie de Sciences Paris, Serie I 339 (2004), 115-118",
  "doi": "10.1016/j.crma.2004.05.008",
  "categories": [
    "math.AP"
  ],
  "abstract": "Pseudo-differential operators of type 1,1 are proved continuous from the Triebel--Lizorkin space $F^d_{p,1}$ to $L_p$ for $1\\le p<\\infty$, when of order d, and this is the largest possible domain among the Besov and Triebel--Lizorkin spaces. H\\\"ormander's condition on the twisted diagonal is extended to this framework, using a general support rule for Fourier transformed pseudo-differential operators.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-02-07T14:24:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47G30",
      "46E35"
    ],
    "keywords": [
      "triebel-lizorkin space",
      "fourier transformed pseudo-differential operators",
      "general support rule"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Elsevier"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}