{
  "id": "2010.13895",
  "version": "v1",
  "published": "2020-10-26T21:04:11.000Z",
  "updated": "2020-10-26T21:04:11.000Z",
  "title": "Rough pseudodifferential operators on Hardy spaces for Fourier integral operators",
  "authors": [
    "Jan Rozendaal"
  ],
  "comment": "23 pages",
  "categories": [
    "math.AP",
    "math.CA"
  ],
  "abstract": "We prove mapping properties of pseudodifferential operators with rough symbols on Hardy spaces for Fourier integral operators. The symbols $a(x,\\eta)$ are elements of $C^{r}_{*}S^{m}_{1,\\delta}$ classes that have limited regularity in the $x$ variable. We show that the associated pseudodifferential operator $a(x,D)$ maps between Sobolev spaces $\\mathcal{H}^{p,s}_{FIO}(\\mathbb{R}^{n})$ and $\\mathcal{H}^{p,t}_{FIO}(\\mathbb{R}^{n})$ over the Hardy space for Fourier integral operators $\\mathcal{H}^{p}_{FIO}(\\mathbb{R}^{n})$. Our main result implies that for $m=0$, $\\delta=1/2$ and $r>n-1$, $a(x,D)$ acts boundedly on $\\mathcal{H}^{p}_{FIO}(\\mathbb{R}^{n})$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-10-26T21:04:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35S05",
      "42B35",
      "35S30",
      "35S50"
    ],
    "keywords": [
      "fourier integral operators",
      "hardy space",
      "rough pseudodifferential operators",
      "main result implies",
      "sobolev spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}