{
  "id": "1702.01070",
  "version": "v1",
  "published": "2017-02-03T16:18:15.000Z",
  "updated": "2017-02-03T16:18:15.000Z",
  "title": "Domains of pseudo-differential operators: a case for the Triebel--Lizorkin spaces",
  "authors": [
    "Jon Johnsen"
  ],
  "comment": "20 pages. Final version from 2005, under open access by Hindawi",
  "journal": "Journal of function spaces and applications, vol. 3, no. 3, 263--286 (2005",
  "doi": "10.1155/2005/393050",
  "categories": [
    "math.AP"
  ],
  "abstract": "The main result is that every pseudo-differential operator of type 1,1 and order $d$ is continuous from the Triebel--Lizorkin space $F^d_{p,1}$ to $L_p$, $1\\le p<\\infty$, and that this is optimal within the Besov and Triebel--Lizorkin scales.The proof also leads to the known continuity for $s>d$, while for all real $s$ the sufficiency of H\\\"ormander's condition on the twisted diagonal is carried over to the Besov and Triebel--Lizorkin framework. To obtain this, type 1,1-operators are extended to distributions with compact spectrum, and Fourier transformed operators of this type are on such distributions proved to satisfy a support rule, generalising the rule for convolutions. Thereby the use of reduced symbols, as introduced by Coifman and Meyer, is replaced by direct application of the paradifferential methods. A few flaws in the literature have been detected and corrected.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-02-03T16:18:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47G30",
      "46E35"
    ],
    "keywords": [
      "pseudo-differential operator",
      "triebel-lizorkin space",
      "main result",
      "triebel-lizorkin framework",
      "paradifferential methods"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Hindawi",
      "journal": "Adv. High Energ. Phys."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}