{
  "id": "1905.13477",
  "version": "v1",
  "published": "2019-05-31T09:31:08.000Z",
  "updated": "2019-05-31T09:31:08.000Z",
  "title": "$L\\log \\log L$ versions of Stein's and Zygmund's theorems for the Hardy space $H^{\\log}(\\mathbb{R}^d)$",
  "authors": [
    "Odysseas Bakas",
    "Salvador Rodríguez-López",
    "Alan Sola"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "We obtain versions of some classical results of Zygmund and Stein for functions belonging to the Hardy space $H^{\\log} (\\mathbb{R}^d)$ introduced by Bonami, Grellier, and Ky. We present further applications in the context of more general Orlicz spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-05-31T09:31:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B25",
      "42B35",
      "46E30"
    ],
    "keywords": [
      "hardy space",
      "zygmunds theorems",
      "general orlicz spaces",
      "applications",
      "classical results"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}