{
  "id": "1908.01448",
  "version": "v1",
  "published": "2019-08-05T02:42:51.000Z",
  "updated": "2019-08-05T02:42:51.000Z",
  "title": "Characterizations of the Hardy space $\\mathcal{H}_{FIO}^{1}(\\mathbb{R}^{n})$ for Fourier Integral Operators",
  "authors": [
    "Zhijie Fan",
    "Naijia Liu",
    "Jan Rozendaal",
    "Liang Song"
  ],
  "comment": "18 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "The Hardy spaces for Fourier integral operators $\\mathcal{H}_{FIO}^{p}(\\mathbb{R}^{n})$, for $1\\leq p\\leq \\infty$, were introduced by H.~Smith in \\cite{Smith98a} and A.~Hassell et al.~in \\cite{HaPoRo18}. In this article, we give several equivalent characterizations of $\\mathcal{H}_{FIO}^{1}(\\mathbb{R}^{n})$, for example in terms of Littlewood--Paley g functions and maximal functions. This answers a question from [Rozendaal,2019].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-08-05T02:42:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35S30",
      "42B30"
    ],
    "keywords": [
      "fourier integral operators",
      "hardy space",
      "equivalent characterizations",
      "maximal functions",
      "littlewood-paley"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}