{
  "id": "1811.08881",
  "version": "v1",
  "published": "2018-11-21T18:53:46.000Z",
  "updated": "2018-11-21T18:53:46.000Z",
  "title": "Littlewood--Paley characterizations of $\\mathrm{BMO}$ and Triebel--Lizorkin spaces",
  "authors": [
    "Anton Tselishchev",
    "Ioann Vasilyev"
  ],
  "journal": "Mathematische Nachrichten. 2020; 293: 2029--2043",
  "doi": "10.1002/mana.201900059",
  "categories": [
    "math.CA"
  ],
  "abstract": "We prove one generalization of the Littlewood--Paley characterization of the $\\mathrm{BMO}$ space where the dilations of a Schwartz function are replaced by a family of functions with suitable conditions imposed on them. We also prove that a certain family of Triebel--Lizorkin spaces can be characterized in a similar way.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-11-21T18:53:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B25"
    ],
    "keywords": [
      "triebel-lizorkin spaces",
      "littlewood-paley characterization",
      "schwartz function",
      "similar way"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}