{
  "id": "1210.6237",
  "version": "v2",
  "published": "2012-10-23T14:00:30.000Z",
  "updated": "2014-06-08T22:41:15.000Z",
  "title": "Heat kernel based decomposition of spaces of distributions in the framework of Dirichlet spaces",
  "authors": [
    "Gerard Kerkyacharian",
    "Pencho Petrushev"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "Classical and non classical Besov and Triebel-Lizorkin spaces with complete range of indices are developed in the general setting of Dirichlet space with a doubling measure and local scale-invariant Poincar\\'e inequality. This leads to Heat kernel with small time Gaussian bounds and H\\\"older continuity, which play a central role in this article. Frames with band limited elements of sub-exponential space localization are developed, and frame and heat kernel characterizations of Besov and Triebel-Lizorkin spaces are established. This theory, in particular, allows to develop Besov and Triebel-Lizorkin spaces and their frame and heat kernel characterization in the context of Lie groups, Riemannian manifold, and other settings.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-06-08T22:41:15.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "dirichlet space",
      "triebel-lizorkin spaces",
      "heat kernel characterization",
      "small time gaussian bounds",
      "distributions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1210.6237K"
    }
  }
}