{
  "id": "2308.07128",
  "version": "v1",
  "published": "2023-08-14T13:28:25.000Z",
  "updated": "2023-08-14T13:28:25.000Z",
  "title": "Hardy-Littlewood maximal operators on trees with bounded geometry",
  "authors": [
    "Matteo Levi",
    "Stefano Meda",
    "Federico Santagati",
    "Maria Vallarino"
  ],
  "comment": "30 pages",
  "categories": [
    "math.FA",
    "math.CA"
  ],
  "abstract": "In this paper we study the $L^p$ boundedness of the centred and the uncentred Hardy--Littlewood maximal operators on the class $\\Upsilon_{a,b}$, $2\\leq a\\leq b$, of trees with $(a,b)$-bounded geometry. We find the sharp range of $p$, depending on $a$ and $b$, where the centred maximal operator is bounded on $L^p(\\mathfrak T)$ for all $\\mathfrak T$ in $\\Upsilon_{a,b}$. We show that there exists a tree in $\\Upsilon_{a,b}$ for which the uncentred maximal function is bounded on $L^p$ if and only if $p=\\infty$. We also extend these results to graphs which are strictly roughly isometric, in the sense of Kanai, to trees in the class $\\Upsilon_{a,b}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-08-14T13:28:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "bounded geometry",
      "uncentred hardy-littlewood maximal operators",
      "centred maximal operator",
      "uncentred maximal function",
      "sharp range"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}