{
  "id": "1803.07865",
  "version": "v1",
  "published": "2018-03-21T11:43:45.000Z",
  "updated": "2018-03-21T11:43:45.000Z",
  "title": "Norm Estimates for $τ$-Pseudodifferential Operators in Wiener Amalgam and Modulation Spaces",
  "authors": [
    "Elena Cordero",
    "Lorenza D'Elia",
    "Salvatore Ivan Trapasso"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "We study continuity properties on modulation spaces for $\\tau$-pseudodifferential operators with symbols $a$ in Wiener amalgam spaces. We obtain boundedness results for $\\tau \\in (0,1)$ whereas, in the end-points $\\tau=0$ and $\\tau=1$, the corresponding operators are in general unbounded. Furthermore, for $\\tau \\in (0,1)$, we exhibit a function of $\\tau$ which is an upper bound for the operator norm. The continuity properties of $\\tau$-pseudodifferential operators, for any $\\tau\\in [0,1]$, with symbols $a$ in modulation spaces are well known. Here we find an upper bound for the operator norm which does not depend on the parameter $\\tau \\in [0,1]$, as expected. Key ingredients are uniform continuity estimates for $\\tau$-Wigner distributions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-03-21T11:43:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47G30",
      "35S05",
      "42B35",
      "81S30"
    ],
    "keywords": [
      "modulation spaces",
      "pseudodifferential operators",
      "norm estimates",
      "upper bound",
      "operator norm"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}