{
  "id": "2012.02872",
  "version": "v1",
  "published": "2020-12-04T22:07:15.000Z",
  "updated": "2020-12-04T22:07:15.000Z",
  "title": "Notes on $H^{\\log} $: structural properties, dyadic variants, and bilinear $H^1$-$BMO$ mappings",
  "authors": [
    "Odysseas Bakas",
    "Sandra Pott",
    "Salvador Rodríguez-López",
    "Alan Sola"
  ],
  "comment": "This article supersedes and extends a previous article arXiv:1905.13477",
  "categories": [
    "math.CA"
  ],
  "abstract": "This article is devoted to a study of the Hardy space $H^{\\log} (\\mathbb{R}^d)$ introduced by Bonami, Grellier, and Ky. We present an alternative approach to their result relating the product of a function in the real Hardy space $H^1$ and a function in $BMO$ to distributions that belong to $H^{\\log}$ based on dyadic paraproducts. We also point out analogues of classical results of Hardy-Littlewood, Zygmund, and Stein for $H^{\\log}$ and related Musielak-Orlicz spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-12-04T22:07:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B35",
      "42B25",
      "42C40"
    ],
    "keywords": [
      "dyadic variants",
      "structural properties",
      "real hardy space",
      "related musielak-orlicz spaces",
      "dyadic paraproducts"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}