{
  "id": "2202.09944",
  "version": "v2",
  "published": "2022-02-21T01:37:58.000Z",
  "updated": "2022-02-23T14:17:56.000Z",
  "title": "Sparse domination and $L^{p} \\rightarrow L^{q}$ estimates for maximal functions associated with curvature",
  "authors": [
    "Wenjuan Li",
    "Huiju Wang",
    "Yujia Zhai"
  ],
  "categories": [
    "math.CA",
    "math.FA"
  ],
  "abstract": "In this paper, we study maximal functions along some finite type curves and hypersurfaces. In particular, various impacts of non-isotropic dilations are considered. Firstly, we provide a generic scheme that allows us to deduce the sparse domination bounds for global maximal functions under the assumption that the corresponding localized maximal functions satisfy the $L^{p}$ improving properties. Secondly, for the localized maximal functions with non-isotropic dilations of curves and hypersurfaces whose curvatures vanish to finite order at some points, we establish the $L^{p}\\rightarrow L^{q}$ bounds $(q >p)$. As a corollary, we obtain the weighted inequalities for the corresponding global maximal functions, which generalize the known unweighted estimates.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2022-02-23T14:17:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B20",
      "42B25"
    ],
    "keywords": [
      "non-isotropic dilations",
      "corresponding localized maximal functions satisfy",
      "sparse domination bounds",
      "corresponding global maximal functions",
      "finite type curves"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}