{
  "id": "2402.04993",
  "version": "v1",
  "published": "2024-02-07T16:11:40.000Z",
  "updated": "2024-02-07T16:11:40.000Z",
  "title": "Off-diagonal compactness extrapolation principles for commutators",
  "authors": [
    "Tuomas Oikari"
  ],
  "comment": "9 pages",
  "categories": [
    "math.CA",
    "math.FA"
  ],
  "abstract": "We provide new off-diagonal compactness extrapolation principles for commutators of bounded singular integral operators, both of Calder\\'on-Zygmund and of rough type. These principles unify the existing theory by streamlining the current state-of-the-art proofs. In particular, we apply them to show that the sufficient conditions for the $L^p$-to-$L^q$ compactness of commutators in the ranges $q>p$ (recently due to Guo et al.) and $q = p$ (classical, due to Uchiyama) and $q<p$ (recently, due to Hyt\\\"onen et al.) all quickly follow from each other.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-02-07T16:11:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B20",
      "47B47"
    ],
    "keywords": [
      "off-diagonal compactness extrapolation principles",
      "commutators",
      "bounded singular integral operators",
      "current state-of-the-art proofs",
      "rough type"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}