{
  "id": "2308.16214",
  "version": "v1",
  "published": "2023-08-30T16:10:37.000Z",
  "updated": "2023-08-30T16:10:37.000Z",
  "title": "Characterizations of the mixed central Campanato spaces via the commutator operators of Hardy type",
  "authors": [
    "Wenna Lu",
    "Jiang Zhou"
  ],
  "comment": "22 pages. arXiv admin note: text overlap with arXiv:2308.16108",
  "categories": [
    "math.FA"
  ],
  "abstract": "The purpose of this paper is to establish some characterizations of mixed central Campanato space $\\mathfrak{C}^{\\vec{p},\\lambda}(\\mathbb{R}^{n})$, via the boundedness of the commutator operators of Hardy type. Unlike the case $\\lambda\\geq0$, there are some technical difficulties caused by $\\lambda<0$ to be overcome. In addition, an extra assumption called as the mixed version of the reverse H\\\"{o}lder class be required in the proof of the converse characterization. Moreover, some further interesting conclusions for the Hardy type operators on mixed $\\lambda$-central Morrey space $\\mathcal{B}^{\\vec{p},\\lambda}(\\mathbb{R}^{n})$ are also derived.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-08-30T16:10:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B20",
      "42B25",
      "42B35"
    ],
    "keywords": [
      "mixed central campanato space",
      "commutator operators",
      "central morrey space",
      "hardy type operators",
      "converse characterization"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}