{
  "id": "1606.01064",
  "version": "v1",
  "published": "2016-06-03T12:40:47.000Z",
  "updated": "2016-06-03T12:40:47.000Z",
  "title": "Hardy spaces for semigroups with Gaussian bounds",
  "authors": [
    "Jacek Dziubański",
    "Marcin Preisner"
  ],
  "categories": [
    "math.FA",
    "math.CA"
  ],
  "abstract": "Let T_t=e^{-tL} be a semigroup of self-adjoint linear operators acting on L^2(X,mu), where (X,d mu) is a space of homogeneous type. We assume that T_t has an integral kernel T_t(x,y) which satisfies the upper and lower Gaussian bounds: \\frac{C_1}{mu(B(x,\\sqrt{t}))} \\exp(-c_1d(x,y)^2/t)\\leq T_t(x,y) \\leq \\frac{C_2}{\\mu(B(x,\\sqrt{t}))} \\exp(-c_2 d(x,y)^2/t). By definition, f belongs to H^1_L if \\| f\\|_{H^1_L}=\\|\\sup_{t>0}|T_t f(x)|\\|_{L^1(X,\\mu)} <\\infty. We prove that there is a function \\omega(x), 0<c \\leq \\omega(x) \\leq C, such that H^1_L admits an atomic decomposition with atoms satisfying: supp a \\subset B, \\|a\\|_{L^\\infty} \\leq mu(B)^{-1}, and the weighted cancellation condition \\int a(x)\\omega(x) dmu(x)=0.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-06-03T12:40:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B30",
      "42B25",
      "42B35",
      "35J10"
    ],
    "keywords": [
      "hardy spaces",
      "lower gaussian bounds",
      "self-adjoint linear operators acting",
      "weighted cancellation condition",
      "atomic decomposition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}