{
  "id": "1902.00096",
  "version": "v1",
  "published": "2019-01-31T22:11:15.000Z",
  "updated": "2019-01-31T22:11:15.000Z",
  "title": "A maximal function for families of Hilbert transforms along homogeneous curves",
  "authors": [
    "Shaoming Guo",
    "Joris Roos",
    "Andreas Seeger",
    "Po-Lam Yung"
  ],
  "comment": "43 pages, submitted",
  "categories": [
    "math.CA"
  ],
  "abstract": "Let $H^{(u)}$ be the Hilbert transform along the parabola $(t, ut^2)$ where $u\\in \\mathbb R$. For a set $U$ of positive numbers consider the maximal function $\\mathcal{H}^U \\!f= \\sup\\{|H^{(u)}\\! f|: u\\in U\\}$. We obtain an (essentially) optimal result for the $L^p$ operator norm of $\\mathcal{H}^U$ when $2<p<\\infty$. The results are proved for families of Hilbert transforms along more general nonflat homogeneous curves.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-01-31T22:11:15.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hilbert transform",
      "maximal function",
      "general nonflat homogeneous curves",
      "operator norm",
      "optimal result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 43,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}