{
  "id": "0802.3128",
  "version": "v1",
  "published": "2008-02-21T15:10:44.000Z",
  "updated": "2008-02-21T15:10:44.000Z",
  "title": "$L^p$ Boundedness of Commutators of Riesz Transforms associated to Schrödinger Operator",
  "authors": [
    "Zihua Guo",
    "Pengtao Li",
    "Lizhong Peng"
  ],
  "comment": "14 pages, 0 figures",
  "journal": "J. Math. Anal. Appl. 341 (2008) 421-432",
  "categories": [
    "math.CA"
  ],
  "abstract": "In this paper we consider $L^p$ boundedness of some commutators of Riesz transforms associated to Schr\\\"{o}dinger operator $P=-\\Delta+V(x)$ on $\\mathbb{R}^n, n\\geq 3$. We assume that $V(x)$ is non-zero, nonnegative, and belongs to $B_q$ for some $q \\geq n/2$. Let $T_1=(-\\Delta+V)^{-1}V,\\ T_2=(-\\Delta+V)^{-1/2}V^{1/2}$ and $T_3=(-\\Delta+V)^{-1/2}\\nabla$. We obtain that $[b,T_j] (j=1,2,3)$ are bounded operators on $L^p(\\mathbb{R}^n)$ when $p$ ranges in a interval, where $b \\in \\mathbf{BMO}(\\mathbb{R}^n)$. Note that the kernel of $T_j (j=1,2,3)$ has no smoothness.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-02-21T15:10:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47B38",
      "42B25",
      "35Q40"
    ],
    "keywords": [
      "riesz transforms",
      "schrödinger operator",
      "boundedness",
      "commutators",
      "smoothness"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1016/j.jmaa.2007.05.024",
      "journal": "Journal of Mathematical Analysis and Applications",
      "year": 2008,
      "month": "May",
      "volume": 341,
      "number": 1,
      "pages": 421
    },
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008JMAA..341..421G"
    }
  }
}