{
  "id": "0904.1691",
  "version": "v1",
  "published": "2009-04-10T14:04:10.000Z",
  "updated": "2009-04-10T14:04:10.000Z",
  "title": "Pseudodifferential operators on $L^p$, Wiener amalgam and modulation spaces",
  "authors": [
    "Elena Cordero",
    "Fabio Nicola"
  ],
  "comment": "27 pages",
  "categories": [
    "math.AP",
    "math.FA"
  ],
  "abstract": "We give a complete characterization of the continuity of pseudodifferential operators with symbols in modulation spaces $M^{p,q}$, acting on a given Lebesgue space $L^r$. Namely, we find the full range of triples $(p,q,r)$, for which such a boundedness occurs. More generally, we completely characterize the same problem for operators acting on Wiener amalgam space $W(L^r,L^s)$ and even on modulation spaces $M^{r,s}$. Finally the action of pseudodifferential operators with symbols in $W(\\Fur L^1,L^\\infty)$ is also investigated.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-04-10T14:04:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35S05",
      "46E30"
    ],
    "keywords": [
      "modulation spaces",
      "pseudodifferential operators",
      "wiener amalgam space",
      "lebesgue space",
      "full range"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0904.1691C"
    }
  }
}