{
  "id": "1204.3041",
  "version": "v2",
  "published": "2012-04-13T16:28:13.000Z",
  "updated": "2013-11-14T02:39:34.000Z",
  "title": "Bilinear decompositions for the product space $H^1_L\\times BMO_L$",
  "authors": [
    "Luong Dang Ky"
  ],
  "comment": "Math.Nachr. (to appear)",
  "categories": [
    "math.CA"
  ],
  "abstract": "In this paper, we improve a recent result by Li and Peng on products of functions in $H_L^1(\\bR^d)$ and $BMO_L(\\bR^d)$, where $L=-\\Delta+V$ is a Schr\\\"odinger operator with $V$ satisfying an appropriate reverse H\\\"older inequality. More precisely, we prove that such products may be written as the sum of two continuous bilinear operators, one from $H_L^1(\\bR^d)\\times BMO_L(\\bR^d) $ into $L^1(\\bR^d)$, the other one from $H^1_L(\\bR^d)\\times BMO_L(\\bR^d) $ into $H^{\\log}(\\bR^d)$, where the space $H^{\\log}(\\bR^d)$ is the set of distributions $f$ whose grand maximal function $\\mathfrak Mf$ satisfies $$\\int_{\\mathbb R^d} \\frac {|\\mathfrak M f(x)|}{\\log (e+ |\\mathfrak Mf(x)|)+ \\log(e+|x|)}dx <\\infty.$$",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-11-14T02:39:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J10",
      "42B35"
    ],
    "keywords": [
      "bilinear decompositions",
      "product space",
      "grand maximal function",
      "appropriate reverse",
      "continuous bilinear operators"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1204.3041D"
    }
  }
}