{
  "id": "1202.2063",
  "version": "v2",
  "published": "2012-02-09T17:48:46.000Z",
  "updated": "2012-09-27T00:42:46.000Z",
  "title": "Weighted Hardy spaces associated to operators and boundedness of singular integrals",
  "authors": [
    "The Anh Bui",
    "Xuan Thinh Duong"
  ],
  "comment": "26 pages, some minor errors were corrected",
  "categories": [
    "math.CA"
  ],
  "abstract": "Let $(X, d, \\mu)$ be a space of homogeneous type, i.e. the measure $\\mu$ satisfies doubling (volume) property with respect to the balls defined by the metric $d$. Let $L$ be a non-negative self-adjoint operator on $L^2(X)$. Assume that the semigroup of $L$ satisfies the Davies-Gaffney estimates. In this paper, we study the weighted Hardy spaces $H^p_{L,w}(X)$, $0 < p \\le 1$, associated to the operator $L$ on the space $X$. We establish the atomic and the molecular characterizations of elements in $H^p_{L,w}(X)$. As applications, we obtain the boundedness on $\\HL$ for the generalized Riesz transforms associated to $L$ and for the spectral multipliers of $L$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-09-27T00:42:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B20",
      "35B65",
      "35K05",
      "42B25",
      "47B38",
      "58J35"
    ],
    "keywords": [
      "weighted hardy spaces",
      "singular integrals",
      "boundedness",
      "non-negative self-adjoint operator",
      "davies-gaffney estimates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1202.2063B"
    }
  }
}