{
  "id": "2309.00068",
  "version": "v1",
  "published": "2023-08-31T18:14:55.000Z",
  "updated": "2023-08-31T18:14:55.000Z",
  "title": "The critical weighted inequalities of the spherical maximal function",
  "authors": [
    "Juyoung Lee"
  ],
  "comment": "14 pages",
  "categories": [
    "math.CA"
  ],
  "abstract": "Weighted inequality on the Hardy-Littlewood maximal function is completely understood while it is not well understood for the spherical maximal function. For the power weight $|x|^{\\alpha}$, it is known that the spherical maximal operator on $\\mathbb{R}^d$ is bounded on $L^p(|x|^{\\alpha})$ only if $1-d\\leq \\alpha<(d-1)(p-1)-d$ and under this condition, it is known to be bounded except $\\alpha=1-d$. In this paper, we prove the case of the critical order, $\\alpha=1-d$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-08-31T18:14:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B25",
      "35S30"
    ],
    "keywords": [
      "spherical maximal function",
      "critical weighted inequalities",
      "weighted inequality",
      "hardy-littlewood maximal function",
      "understood"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}