{
  "id": "2406.03382",
  "version": "v1",
  "published": "2024-06-05T15:33:47.000Z",
  "updated": "2024-06-05T15:33:47.000Z",
  "title": "Self-improving boundedness of the maximal operator on quasi-Banach lattices over spaces of homogeneous type",
  "authors": [
    "Alina Shalukhina"
  ],
  "comment": "19 pages",
  "categories": [
    "math.CA",
    "math.FA"
  ],
  "abstract": "We prove the self-improvement property of the Hardy--Littlewood maximal operator on quasi-Banach lattices with the Fatou property in the setting of spaces of homogeneous type. Our result is a generalization of the boundedness criterion obtained in 2010 by Lerner and Ombrosi for maximal operators on quasi-Banach function spaces over Euclidean spaces. The specialty of the proof for spaces of homogeneous type lies in using adjacent grids of Hyt\\\"onen--Kairema dyadic cubes and studying the maximal operator alongside its dyadic version. Then we apply the obtained result to variable Lebesgue spaces over spaces of homogeneous type.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-06-05T15:33:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B25",
      "46E30",
      "30L99",
      "43A99"
    ],
    "keywords": [
      "homogeneous type",
      "quasi-banach lattices",
      "self-improving boundedness",
      "hardy-littlewood maximal operator",
      "maximal operator alongside"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}