{
  "id": "1709.03127",
  "version": "v1",
  "published": "2017-09-10T16:34:27.000Z",
  "updated": "2017-09-10T16:34:27.000Z",
  "title": "Some jump and variational inequalities for the Calderón commutators and related operators",
  "authors": [
    "Yanping Chen",
    "Yong Ding",
    "Guixiang Hong",
    "Jie Xiao"
  ],
  "comment": "44 pages",
  "categories": [
    "math.CA"
  ],
  "abstract": "In this paper, we establish jump and variational inequalities for the Calder\\'{o}n commutators, which are typical examples of non-convolution Calder\\'on-Zygmund operators. For this purpose, we also show jump and variational inequalities for para-products and commutators from pseudo-differential calculus, which are of independent interest. New ingredients in the proofs involve identifying Carleson measures constructed from sequences of stopping times, in addition to many Littlewood-Paley type estimates with gradient.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-09-10T16:34:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B20",
      "42B25"
    ],
    "keywords": [
      "variational inequalities",
      "calderón commutators",
      "related operators",
      "non-convolution calderon-zygmund operators",
      "littlewood-paley type estimates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 44,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}