{
  "id": "2405.20907",
  "version": "v1",
  "published": "2024-05-31T15:18:08.000Z",
  "updated": "2024-05-31T15:18:08.000Z",
  "title": "The Muckenhoupt condition",
  "authors": [
    "Zoe Nieraeth"
  ],
  "comment": "38 pages",
  "categories": [
    "math.FA",
    "math.CA"
  ],
  "abstract": "The goal of this paper is to unify the theory of weights beyond the setting of weighted Lebesgue spaces in the general setting of quasi-Banach function spaces. We prove new characterizations for the boundedness of singular integrals, and pose several conjectures and partial results related to the duality of the Hardy-Littlewood maximal operator. Furthermore, we give an overview of the theory applied to weighted variable Lebesgue and Morrey spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-05-31T15:18:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B25",
      "46E30"
    ],
    "keywords": [
      "muckenhoupt condition",
      "hardy-littlewood maximal operator",
      "quasi-banach function spaces",
      "partial results",
      "weighted lebesgue spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 38,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}