{
  "id": "2102.02105",
  "version": "v1",
  "published": "2021-02-03T15:18:24.000Z",
  "updated": "2021-02-03T15:18:24.000Z",
  "title": "On weighted Compactness of Commutator of semi-group maximal function associated to Schrödinger operators",
  "authors": [
    "Shifen Wang",
    "Qingying Xue"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:2012.12747",
  "categories": [
    "math.CA",
    "math.AP"
  ],
  "abstract": "Let $\\mathcal{T}^*$ be the semi-group maximal function associated to the Schr\\\"odinger operator $-\\Delta+V(x)$ with $V$ satisfying an appropriate reverse H\\\"{o}lder inequality. In this paper, we show that the commutator of $\\mathcal{T}^*$ is a compact operator on $L^p(w)$ for $1<p<\\infty$ if $b\\in \\text{CMO}_\\theta(\\rho)(\\mathbb{R}^n)$ and $w\\in A_p^{\\rho,\\theta}(\\mathbb{R}^n)$. Here $\\text{ CMO}_\\theta(\\rho)(\\mathbb{R}^n)$ denotes the closure of $\\mathcal{C}_c^\\infty(\\mathbb{R}^n)$ in the $\\text{BMO}_\\theta(\\rho)(\\mathbb{R}^n)$ (which is larger than the classical $\\text{BMO}(\\mathbb{R}^n)$ space) topology. The space where $b$ belongs and the weighs class $w$ belongs are more larger than the usual $\\text{CMO}(\\mathbb{R}^n)$ space and the Muckenhoupt $A_p$ weights class, respectively.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-02-03T15:18:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B25"
    ],
    "keywords": [
      "semi-group maximal function",
      "schrödinger operators",
      "weighted compactness",
      "commutator",
      "appropriate reverse"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}