{
  "id": "2212.00681",
  "version": "v1",
  "published": "2022-11-24T20:08:05.000Z",
  "updated": "2022-11-24T20:08:05.000Z",
  "title": "Bounded Mean Oscillation: an $\\mathbb{R}$-Function with Multi-$\\mathbb{K}_6$ Cubes. Dual of the Hardy Space $H^1$ and Banach Extent",
  "authors": [
    "Edoardo Niccolai"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "This paper investigates the concept of harmonic functions of bounded mean oscillation, starting from John-Nirenberg's pioneering studies, under a renewed formalism, suitable for bringing out some fundamental properties inherent in it. In more detail: after a quick introduction, the second Section presents the main theorem, plus complete proof, relating to this function; in the third Section there is a suggestion on the exponential integrability (theorem and sketch of proof), while the fourth Section deals with the duality of Hardy Space $H^1$ and bounded mean oscillation, with some ideas for a demonstration. The writing closes with a graphic appendix.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-11-24T20:08:05.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "bounded mean oscillation",
      "hardy space",
      "banach extent",
      "fundamental properties inherent",
      "plus complete proof"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}