{
  "id": "2207.00917",
  "version": "v1",
  "published": "2022-07-02T23:18:18.000Z",
  "updated": "2022-07-02T23:18:18.000Z",
  "title": "New John--Nirenberg--Campanato-Type Spaces Related to Both Maximal Functions and Their Commutators",
  "authors": [
    "Pingxu Hu",
    "Jin Tao",
    "Dachun Yang"
  ],
  "comment": "32 pages, Submitted",
  "categories": [
    "math.FA",
    "math.AP",
    "math.CA"
  ],
  "abstract": "Let $p,q\\in [1,\\infty]$, $\\alpha\\in{\\mathbb{R}}$, and $s$ be a non-negative integer. In this article, the authors introduce a new function space $\\widetilde{JN}_{(p,q,s)_{\\alpha}}(\\mathcal{X})$ of John-Nirenberg-Campanato type, where $\\mathcal{X}$ denotes $\\mathbb{R}^n$ or any cube $Q_{0}$ of $\\mathbb{R}^n$ with finite edge length. The authors give an equivalent characterization of $\\widetilde{JN}_{(p,q,s)_{\\alpha}}(\\mathcal{X})$ via both the John-Nirenberg-Campanato space and the Riesz-Morrey space. Moreover, for the particular case $s=0$, this new space can be equivalently characterized by both maximal functions and their commutators. Additionally, the authors give some basic properties, a good-$\\lambda$ inequality, and a John-Nirenberg type inequality for $\\widetilde{JN}_{(p,q,s)_{\\alpha}}(\\mathcal{X})$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-07-02T23:18:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B35",
      "47B47",
      "46E30",
      "42B25"
    ],
    "keywords": [
      "maximal functions",
      "john-nirenberg-campanato-type spaces",
      "commutators",
      "john-nirenberg type inequality",
      "finite edge length"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}