{
  "id": "2103.08227",
  "version": "v1",
  "published": "2021-03-15T09:21:13.000Z",
  "updated": "2021-03-15T09:21:13.000Z",
  "title": "Wavelet Characterization of Besov and Triebel--Lizorkin Spaces on Spaces of Homogeneous Type and Its Applications",
  "authors": [
    "Ziyi He",
    "Fan Wang",
    "Dachun Yang",
    "Wen Yuan"
  ],
  "comment": "55 pages, Submitted",
  "categories": [
    "math.FA",
    "math.AP",
    "math.CA"
  ],
  "abstract": "In this article, the authors establish the wavelet characterization of Besov and Triebel--Lizorkin spaces on a given space $(X,d,\\mu)$ of homogeneous type in the sense of Coifman and Weiss. Moreover, the authors introduce almost diagonal operators on Besov and Triebel--Lizorkin sequence spaces on $X$, and obtain their boundedness. Using this wavelet characterization and this boundedness of almost diagonal operators, the authors obtain the molecular characterization of Besov and Triebel--Lizorkin spaces. Applying this molecular characterization, the authors further establish the Littlewood--Paley characterizations of Triebel--Lizorkin spaces on $X$. The main novelty of this article is that all these results get rid of their dependence on the reverse doubling property of $\\mu$ and also the triangle inequality of $d$, by fully using the geometrical property of $X$ expressed via its equipped quasi-metric $d$, dyadic reference points, dyadic cubes, and wavelets",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-03-15T09:21:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46E35",
      "46E36",
      "46E39",
      "42B25",
      "30L99"
    ],
    "keywords": [
      "triebel-lizorkin spaces",
      "wavelet characterization",
      "homogeneous type",
      "diagonal operators",
      "molecular characterization"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 55,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}