{
  "id": "2406.03408",
  "version": "v1",
  "published": "2024-06-05T16:06:47.000Z",
  "updated": "2024-06-05T16:06:47.000Z",
  "title": "A characterization of Calderón-Zygmund operators on RBMO",
  "authors": [
    "Evgueni Doubtsov",
    "Andrei V. Vasin"
  ],
  "comment": "12 pages",
  "categories": [
    "math.FA",
    "math.CA"
  ],
  "abstract": "Let $\\mathrm{RBMO}(\\mu) = \\mathrm{RBMO}(\\mathbb{R}^m, \\mu)$ denote the regular BMO space introduced by X. Tolsa for an $n$-dimensional finite positive measure on $\\mathbb{R}^m$, $0<n \\le m$. We characterize the bounded Calder\\'on-Zygmund operators $T:\\mathrm{RBMO}(\\mu) \\to \\mathrm{RBMO}(\\mu)$ in terms of the function $T1$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-06-05T16:06:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B20",
      "42B35"
    ],
    "keywords": [
      "calderón-zygmund operators",
      "characterization",
      "regular bmo space",
      "dimensional finite positive measure",
      "bounded calderon-zygmund operators"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}