{
  "id": "2104.05380",
  "version": "v1",
  "published": "2021-04-12T11:59:50.000Z",
  "updated": "2021-04-12T11:59:50.000Z",
  "title": "Median-type John-Nirenberg space in metric measure spaces",
  "authors": [
    "Kim Myyryläinen"
  ],
  "comment": "21 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "We study the so-called John-Nirenberg space that is a generalization of functions of bounded mean oscillation in the setting of metric measure spaces with a doubling measure. Our main results are local and global John-Nirenberg inequalities, which give weak type estimates for the oscillation of a function. We consider medians instead of integral averages throughout, and thus functions are not a priori assumed to be locally integrable. Our arguments are based on a Calder\\'{o}n-Zygmund decomposition and a good-$\\lambda$ inequality for medians. A John-Nirenberg inequality up to the boundary is proven by using chaining arguments. As a consequence, the integral-type and the median-type John-Nirenberg spaces coincide under a Boman-type chaining assumption.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-04-12T11:59:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B35",
      "43A85"
    ],
    "keywords": [
      "metric measure spaces",
      "john-nirenberg inequality",
      "median-type john-nirenberg spaces coincide",
      "integral averages throughout",
      "weak type estimates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}