{
  "id": "1906.05997",
  "version": "v1",
  "published": "2019-06-14T03:03:29.000Z",
  "updated": "2019-06-14T03:03:29.000Z",
  "title": "Maximal functions associated with families of homogeneous curves: $L^p$ bounds for $p\\le 2$",
  "authors": [
    "Shaoming Guo",
    "Joris Roos",
    "Andreas Seeger",
    "Po-Lam Yung"
  ],
  "comment": "13 pages",
  "categories": [
    "math.CA"
  ],
  "abstract": "Let $M^{(u)}$, $H^{(u)}$ be the maximal operator and Hilbert transform along the parabola $(t, ut^2) $. For $U\\subset(0,\\infty)$ we consider $L^p$ estimates for the maximal functions $\\sup_{u\\in U}|M^{(u)} f|$ and $\\sup_{u\\in U}|H^{(u)} f|$, when $1<p\\le 2$. The parabolae can be replaced by more general non-flat homogeneous curves.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-06-14T03:03:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B15",
      "42B20",
      "42B25",
      "44A12"
    ],
    "keywords": [
      "maximal functions",
      "general non-flat homogeneous curves",
      "maximal operator",
      "hilbert transform"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}