{
  "id": "2007.10864",
  "version": "v1",
  "published": "2020-07-21T14:43:04.000Z",
  "updated": "2020-07-21T14:43:04.000Z",
  "title": "Weighted norm inequalities for the maximal operator on $\\Lpp$ over spaces of homogeneous type",
  "authors": [
    "David Cruz-Uribe",
    "Jeremy Cummings"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "Given a space of homogeneous type $(X,\\mu,d)$, we prove strong-type weighted norm inequalities for the Hardy-Littlewood maximal operator over the variable exponent Lebesgue spaces $L^\\pp$. We prove that the variable Muckenhoupt condition $\\App$ is necessary and sufficient for the strong type inequality if $\\pp$ satisfies log-H\\\"older continuity conditions and $1 < p_- \\leq p_+ < \\infty$. Our results generalize to spaces of homogeneous type the analogous results in Euclidean space proved by Cruz-Uribe, Fiorenza and Neugebuaer (2012).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-07-21T14:43:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B25",
      "46A80",
      "46E30"
    ],
    "keywords": [
      "homogeneous type",
      "strong type inequality",
      "hardy-littlewood maximal operator",
      "variable exponent lebesgue spaces",
      "strong-type weighted norm inequalities"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}