{
  "id": "2012.12747",
  "version": "v1",
  "published": "2020-12-23T15:29:28.000Z",
  "updated": "2020-12-23T15:29:28.000Z",
  "title": "On weighted Compactness of commutators of bilinear maximal Calderón-Zygmund singular integral operators",
  "authors": [
    "Shifeng Wang",
    "Qingying Xue"
  ],
  "comment": "16 pages",
  "categories": [
    "math.CA"
  ],
  "abstract": "Let $T$ be a bilinear Calder\\'on-Zygmund singular integral operator and $T^*$ be its corresponding truncated maximal operator. For any $b\\in\\text{BMO}(\\mathbb {R}^n)$ and $\\vec{b}=(b_1,\\ b_2)\\in\\text{BMO}(\\mathbb {R}^n)\\times\\text {BMO}(\\mathbb{R}^n)$, let $T^*_{b,j}$ (j=1,2), $T^*_{\\vec{b}}\\ $ be the commutators in the j-th entry and the iterated commutators of $T^*$, respectively. In this paper, for all $1<p_1,p_2<\\infty$, $\\frac{1}{p}=\\frac{1}{p_1}+\\frac{1}{p_2}$, we show that $T^*_{b,j}$ and $T^*_{\\vec{b}}$ are compact operators from $L^{p_1}(w_1)\\times L^{p_2}(w_2)$ to $L^p(v_{\\vec{w}})$, if $b,b_1,b_2\\in{\\rm CMO}(\\mathbb{R}^n)$ and $\\vec{w}=(w_1,w_2)\\in A_{\\vec{p}}$, $v_{\\vec{w}}=w_1^{p/p_1}w_2^{p/p_2}$. Here ${\\rm CMO}(\\mathbb{R}^n)$ denotes the closure of $\\mathcal{C}_c^\\infty(\\mathbb{R}^n)$ in the ${\\rm BMO}(\\mathbb{R}^n)$ topology and $A_{\\vec{p}}$ is the multiple weights class.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-12-23T15:29:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B25"
    ],
    "keywords": [
      "maximal calderón-zygmund singular integral operators",
      "bilinear maximal calderón-zygmund singular integral",
      "weighted compactness",
      "commutators",
      "bilinear calderon-zygmund singular integral operator"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}