{
  "id": "2303.16587",
  "version": "v1",
  "published": "2023-03-29T10:44:59.000Z",
  "updated": "2023-03-29T10:44:59.000Z",
  "title": "Maximal operator in Musielak--Orlicz--Sobolev spaces",
  "authors": [
    "Piotr Michał Bies",
    "Michał Gaczkowski",
    "Przemysław Górka"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "We study the Hardy-Littlewood maximal operator in the Musielak-Orlicz-Sobolev space $W^{1,\\varphi}(\\mathbb{R}^n)$. Under some natural assumptions on $\\varphi$ we show that the maximal function is bounded and continuous in $W^{1,\\varphi}(\\mathbb{R}^n)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-03-29T10:44:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B25",
      "46E35"
    ],
    "keywords": [
      "musielak-orlicz-sobolev space",
      "hardy-littlewood maximal operator",
      "natural assumptions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}