{
  "id": "1002.3319",
  "version": "v3",
  "published": "2010-02-17T17:27:42.000Z",
  "updated": "2011-11-26T12:14:20.000Z",
  "title": "Riesz transform characterization of H^1 spaces associated with certain Laguerre expansions",
  "authors": [
    "Marcin Preisner"
  ],
  "doi": "10.1016/j.jat.2011.10.004",
  "categories": [
    "math.FA"
  ],
  "abstract": "For alpha>0 we consider the system l_k^{(alpha-1)/2}(x) of the Laguerre functions which are eigenfunctions of the differential operator Lf =-\\frac{d^2}{dx^2}f-\\frac{alpha}{x}\\frac{d}{dx}f+x^2 f. We define an atomic Hardy space H^1_{at}(X), which is a subspace of L^1((0,infty), x^alpha dx). Then we prove that the space H^1_{at}(X) is also characterized by the Riesz transform Rf=\\sqrt{\\pi}\\frac{d}{dx}L^{-1/2}f in the sense that f\\in H^1_{at}(X) if and only if f,Rf \\in L^1((0,infty),x^alpha dx).",
  "revisions": [
    {
      "version": "v3",
      "updated": "2011-11-26T12:14:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B30",
      "42B35",
      "42B20"
    ],
    "keywords": [
      "riesz transform characterization",
      "laguerre expansions",
      "atomic hardy space",
      "differential operator lf"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1002.3319P"
    }
  }
}