{
  "id": "2406.06876",
  "version": "v1",
  "published": "2024-06-11T01:37:07.000Z",
  "updated": "2024-06-11T01:37:07.000Z",
  "title": "Boundedness for maximal operators over hypersurfaces in $\\mathbb{R}^3$",
  "authors": [
    "Wenjuan Li",
    "Huiju Wang"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "In this article, we study maximal functions related to hypersurfaces with vanishing Gaussian curvature in $\\mathbb{R}^3$. Firstly, we characterize the $L^p\\rightarrow L^q$ boundedness of local maximal operators along homogeneous hypersurfaces. Moreover, weighted $L^p$-estimates are obtained for the corresponding global operators. Secondly, for a class of hypersurfaces that lack a homogeneous structure and pass through the origin, we attempt to look for other geometric properties instead of height of hypersurfaces to characterize the optimal $L^p$-boundedness of the corresponding global maximal operators.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-06-11T01:37:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B20",
      "42B25"
    ],
    "keywords": [
      "boundedness",
      "corresponding global maximal operators",
      "local maximal operators",
      "study maximal functions",
      "vanishing gaussian curvature"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}