{
  "id": "2402.12582",
  "version": "v2",
  "published": "2024-02-19T22:32:14.000Z",
  "updated": "2024-05-20T19:18:29.000Z",
  "title": "The property $\\log(f) \\in BMO(\\mathbb R^n)$ in terms of Riesz transforms",
  "authors": [
    "Ioann Vasilyev"
  ],
  "comment": "8 pages, no figures; typos in the Abstract corrected",
  "journal": "Journal of Mathematical Sciences, Vol. 202, No. 4, October, 2014",
  "categories": [
    "math.FA"
  ],
  "abstract": "The condition mentioned in the title is equivalent to the representability of $f$ as the quotient $f=v_1/v_2$, where $v_1$ and $v_2$ obey the inequalities $|R_j v_i| \\leq C |v_i|$ for $i=1,2$ and $j=1,\\ldots, n$. Here, $R_1,\\ldots, R_n$ are the Riesz transformations.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2024-05-20T19:18:29.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "riesz transforms",
      "riesz transformations",
      "representability"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}