{
  "id": "2308.16108",
  "version": "v1",
  "published": "2023-08-30T16:04:36.000Z",
  "updated": "2023-08-30T16:04:36.000Z",
  "title": "A characterization of mixed $λ$-central $\\mathrm{BMO}$ space via the commutators of Hardy type operators",
  "authors": [
    "Wenna Lu",
    "Jiang Zhou"
  ],
  "comment": "14 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "In this paper, we give a characterization of mixed $\\lambda$-central bounded mean oscillation space $\\mathrm{CBMO}^{\\vec{q},\\lambda}(\\mathbb{R}^{n})$ via the boundedness of the commutators of $n$-dimensional Hardy operator $\\mathcal{H}$ and its dual operator $\\mathcal{H}^{*}$ on mixed Lebesgue space $L^{\\vec{p}}(\\mathbb{R}^{n})$. In addition, we also establish the boundedness of commutators $\\mathcal{H}_{b}$ and $\\mathcal{H}^{*}_{b}$ generated with $\\mathrm{CBMO}^{\\vec{q},\\lambda}(\\mathbb{R}^{n})$ function $b$ on mixed $\\lambda$-central Morrey space $\\mathcal{B}^{\\vec{q},\\lambda}(\\mathbb{R}^{n})$, respectively.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-08-30T16:04:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B20",
      "42B25",
      "42B35"
    ],
    "keywords": [
      "hardy type operators",
      "commutators",
      "characterization",
      "central bounded mean oscillation space",
      "central morrey space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}