{
  "id": "1310.5787",
  "version": "v3",
  "published": "2013-10-22T03:12:51.000Z",
  "updated": "2013-12-13T07:08:27.000Z",
  "title": "Compactness of commutators of bilinear maximal Calderón-Zygmund singular integral operators",
  "authors": [
    "Yong Ding",
    "Ting Mei",
    "Qingying Xue"
  ],
  "comment": "New version, corrected the fomer mistakes",
  "categories": [
    "math.CA"
  ],
  "abstract": "Let $T$ be a bilinear Calder\\'{o}n-Zygmund singular integral operator and $T_*$ be its corresponding truncated maximal operator. The commutators in the $i$-$th$ entry and the iterated commutators of $T_*$ are defined by $$ T_{\\ast,b,1}(f,g)(x)=\\sup_{\\delta>0}\\bigg|\\iint_{|x-y|+|x-z|>\\delta}K(x,y,z)(b(y)-b(x))f(y)g(z)dydz\\bigg|, $$ $$T_{\\ast,b,2}(f,g)(x)=\\sup_{\\delta>0}\\bigg|\\iint_{|x-y|+|x-z|>\\delta}K(x,y,z)(b(z)-b(x))f(y)g(z)dydz\\bigg|,$$ \\begin{align*} T_{\\ast,(b_1,b_2)}(f,g)(x)=\\sup\\limits_{\\delta>0}\\bigg|\\iint_{|x-y|+|x-z|>\\delta} K(x,y,z)(b_1(y)-b_1(x))(b_2(z)-b_2(x))f(y)g(z)dydz\\bigg|. \\end{align*} In this paper, the compactness of the commutators $T_{\\ast,b,1}$, $T_{\\ast,b,2}$ and $T_{\\ast,(b_1,b_2)}$ on $L^r(\\mathbb{R}^n))$ is established.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-12-13T07:08:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B25",
      "47G10"
    ],
    "keywords": [
      "maximal calderón-zygmund singular integral operators",
      "bilinear maximal calderón-zygmund singular integral",
      "commutators",
      "compactness",
      "corresponding truncated maximal operator"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1310.5787D"
    }
  }
}