{
  "id": "2404.16707",
  "version": "v1",
  "published": "2024-04-25T16:13:57.000Z",
  "updated": "2024-04-25T16:13:57.000Z",
  "title": "A self-improving property of Riesz potentials in BMO",
  "authors": [
    "You-Wei Benson Chen"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "In this paper we prove that for non-negative measurable functions $f$, \\begin{align*} I_\\alpha f \\in BMO(\\mathbb{R}^n) \\text{ if and only if } I_\\alpha f \\in BMO^\\beta(\\mathbb{R}^n) \\text{ for } \\beta \\in (n-\\alpha,n]. \\end{align*} Here $I_\\alpha$ denotes the Riesz potential of order $\\alpha$ and $BMO^\\beta$ represents the space of functions of bounded $\\beta$-dimensional mean oscillation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-04-25T16:13:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "riesz potential",
      "self-improving property",
      "dimensional mean oscillation",
      "represents",
      "non-negative measurable functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}