{
  "id": "1702.04648",
  "version": "v1",
  "published": "2017-02-15T15:18:49.000Z",
  "updated": "2017-02-15T15:18:49.000Z",
  "title": "Weighted Hardy spaces associated with elliptic operators. Part III: Characterizations of $H_L^{p}(w)$ and the weighted Hardy space associated with the Riesz transform",
  "authors": [
    "Cruz Prisuelos-Arribas"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider Muckenhoupt weights $w$, and define weighted Hardy spaces $H^p_{\\mathcal{T}}(w)$, where $\\mathcal{T}$ denotes a conical square function or a non-tangential maximal function defined via the heat or the Poisson semigroup generated by a second order divergence form elliptic operator $L$. In the range $0<p< 1$, we give a molecular characterization of these spaces. Additionally, in the range $p\\in \\mathcal{W}_w(p_-(L),p_+(L))$ we see that these spaces are isomorphic to the $L^p(w)$ spaces. We also consider the Riesz transform $\\nabla L^{-\\frac{1}{2}}$, associated with $L$, and show that the Hardy spaces $H^p_{\\nabla L^{-1/2},q}(w)$ and $H^p_{\\mathcal{S}_{\\mathrm{H}},q}(w)$ are isomorphic, in some range of $p'$s, and $q\\in \\mathcal{W}_w(q_-(L),q_+(L))$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-02-15T15:18:49.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "riesz transform",
      "characterization",
      "second order divergence form elliptic",
      "order divergence form elliptic operator",
      "define weighted hardy spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}