{
  "id": "1902.05686",
  "version": "v1",
  "published": "2019-02-15T05:17:08.000Z",
  "updated": "2019-02-15T05:17:08.000Z",
  "title": "Continuous characterizations of inhomogeneous Besov and Triebel-Lizorkin spaces associated to non-negative self-adjoint operators",
  "authors": [
    "Qing Hong",
    "Guorong Hu"
  ],
  "comment": "30 pages",
  "categories": [
    "math.CA"
  ],
  "abstract": "Let $(M,\\rho,\\mu)$ be a metric measure space satisfying the doubling, reverse doubling and non-collapsing conditions, and $\\mathscr{L}$ be a self-adjoint operator on $L^2 (M, d\\mu)$ whose heat kernel $p_t (x,y)$ satisfy the small-time Gaussian upper bound, H\\\"{o}lder continuity and Markov property. In this paper, we give characterizations of inhomogeneous \"classical\" and \"non-classical\" Besov and Triebel-Lizorkin spaces associated to $\\mathscr{L}$ in terms of continuous Littlewood-Paley and Lusin area functions defined by the heat semigroup, for full range of indices. This extends related classical results for Besov and Triebel-Lizorkin spaces on $\\mathbb{R}^n$ to more general setting, and extends corresponding results of Kerkyacharian and Petrushev [Trans. Amer. Math Soc. 367 (2015), 121-189] to full range of indices.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-02-15T05:17:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46E35",
      "42B25",
      "42B35"
    ],
    "keywords": [
      "triebel-lizorkin spaces",
      "non-negative self-adjoint operators",
      "continuous characterizations",
      "inhomogeneous besov",
      "full range"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}