{
  "id": "2205.01964",
  "version": "v1",
  "published": "2022-05-04T09:08:54.000Z",
  "updated": "2022-05-04T09:08:54.000Z",
  "title": "On weighted Compactness of Commutators of square function and semi-group maximal function associated to Schrodinger operator",
  "authors": [
    "Shifen Wang",
    "Qingying Xue",
    "Chunmei Zhang"
  ],
  "comment": "16 pages. arXiv admin note: text overlap with arXiv:2102.02105",
  "categories": [
    "math.CA"
  ],
  "abstract": "In this paper, the object of our investigation is the following Littlewood-Paley square function $g$ associated with the Schr\\\"odinger operator $L=-\\Delta +V$ which is defined by: $g(f)(x)=\\Big(\\int_{0}^{\\infty}\\Big|\\frac{d}{dt}e^{-tL}(f)(x)\\Big|^2tdt\\Big)^{1/2},$ where $\\Delta$ is the laplacian operator on $\\mathbb{R}^n$ and $V$ is a nonnegative potential. We show that the commutators of $g$ are compact operators from $L^p(w)$ to $L^p(w)$ for $1<p<\\infty$ if $b\\in {\\rm CMO}_\\theta(\\rho)$ and $w\\in A_p^{\\rho,\\theta}$, where ${\\rm CMO}_\\theta(\\rho)$ is the closure of $\\mathcal{C}_c^\\infty(\\mathbb{R}^n)$ in the ${\\rm BMO}_\\theta(\\rho)$ topology which is more larger than the classical ${\\rm CMO}$ space and $A_p^{\\rho,\\theta}$ is a weights class which is more larger than Muckenhoupt $A_p$ weight class. An extra weight condition in a privious weighted compactness result is removed for the commutators of the semi-group maximal function defined by $\\mathcal{T}^*(f)(x)=\\sup_{t>0}|e^{-tL}f(x)|.$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-05-04T09:08:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B25",
      "35J10"
    ],
    "keywords": [
      "semi-group maximal function",
      "weighted compactness",
      "schrodinger operator",
      "commutators",
      "littlewood-paley square function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}