{
  "id": "2103.13774",
  "version": "v1",
  "published": "2021-03-25T11:57:36.000Z",
  "updated": "2021-03-25T11:57:36.000Z",
  "title": "Sharp growth conditions for boundedness of maximal function in generalized Orlicz spaces",
  "authors": [
    "Petteri Harjulehto",
    "Arttu Karppinen"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "We study sharp growth conditions for the boundedness of the Hardy-Littlewood maximal function in the generalized Orlicz spaces. We assume that the generalized Orlicz function $\\phi(x, t)$ satisfies the standard continuity properties (A0), (A1) and (A2). We show that if the Hardy-Littlewood maximal function is bounded from the generalized Orlicz space to itself then $\\phi(x,t)/ t^p$ is almost increasing for large $t$ for some $p>1$. Moreover we show that the Hardy-Littlewood maximal function is bounded from the generalized Orlicz space $L^\\phi(\\mathbb{R}^n)$ to itself if and only if $\\phi$ is weakly equivalent to a generalized Orlicz function $\\psi$ satisfying (A0), (A1) and (A2) for which $\\psi(x,t)/ t^p$ is almost increasing for all $t>0$ and some $p>1$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-03-25T11:57:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46E30"
    ],
    "keywords": [
      "generalized orlicz space",
      "hardy-littlewood maximal function",
      "generalized orlicz function",
      "boundedness",
      "study sharp growth conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}