{
  "id": "1502.06836",
  "version": "v1",
  "published": "2015-02-24T15:34:45.000Z",
  "updated": "2015-02-24T15:34:45.000Z",
  "title": "A characterisation of the Besov-Lipschitz and Triebel-Lizorkin spaces using Poisson like kernels",
  "authors": [
    "Huy-Qui Bui",
    "Timothy Candy"
  ],
  "comment": "40 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "We give a complete characterisation of the spaces $\\dot{B}^{\\alpha}_{p,q}$ and $\\dot{F}^{\\alpha}_{p,q}$ by using a non-smooth kernel satisfying near minimal conditions. The tools used include a Stromberg-Torchinsky type estimate for certain maximal functions and the concept of a distribution of finite growth, inspired by Stein. Moreover, our exposition also makes essential use of a number of refinements of the well-known Calderon reproducing formula. The results are then applied to obtain the characterisation of these spaces via a fractional derivative of the Poisson kernel.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-02-24T15:34:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B25",
      "46E35"
    ],
    "keywords": [
      "triebel-lizorkin spaces",
      "besov-lipschitz",
      "well-known calderon reproducing formula",
      "stromberg-torchinsky type estimate",
      "non-smooth kernel"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 40,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}