{
  "id": "1712.06923",
  "version": "v1",
  "published": "2017-12-19T13:43:36.000Z",
  "updated": "2017-12-19T13:43:36.000Z",
  "title": "On Bloom type estimates for iterated commutators of fractional integrals",
  "authors": [
    "Natalia Accomazzo",
    "Javier C. Martínez-Perales",
    "Israel P. Rivera-Ríos"
  ],
  "comment": "18 pages",
  "categories": [
    "math.CA"
  ],
  "abstract": "In this paper we provide quantitative Bloom type estimates for iterated commutators of fractional integrals improving and extending results from a work of Holmes, Rahm and Spencer. We give new proofs for those inequalities relying upon a new sparse domination that we provide as well in this paper and also in techniques developed in a recent paper due to Lerner, Ombrosi and the third author. We extend as well the necessity established in the work of Holmes, Rahm and Spencer to iterated commutators providing a new proof. As a consequence of the preceding results we recover the one weight estimates in works of Cruz-Uribe and Moen and B\\'enyi, Martell, Moen, Stachura, Torres and establish the sharpness in the iterated case. Our result provides as well a new characterization of the BMO space.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-12-19T13:43:36.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "iterated commutators",
      "fractional integrals",
      "quantitative bloom type estimates",
      "sparse domination",
      "third author"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}