{
  "id": "1610.01506",
  "version": "v1",
  "published": "2016-10-05T16:22:05.000Z",
  "updated": "2016-10-05T16:22:05.000Z",
  "title": "Factorization in mixed norm Hardy and BMO spaces",
  "authors": [
    "Richard Lechner"
  ],
  "comment": "29 pages, 8 figures",
  "categories": [
    "math.FA"
  ],
  "abstract": "Let $1\\leq p,q < \\infty$ and $1\\leq r \\leq \\infty$. We show that the direct sum of mixed norm Hardy spaces $\\big(\\sum_n H^p_n(H^q_n)\\big)_r$ and the sum of their dual spaces $\\big(\\sum_n H^p_n(H^q_n)^*\\big)_r$ are both primary. We do so by using Bourgain's localization method and solving the finite dimensional factorization problem. In particular, we obtain that the spaces $\\big(\\sum_{n\\in \\mathbb N} H_n^1(H_n^s)\\big)_r$, $\\big(\\sum_{n\\in \\mathbb N} H_n^s(H_n^1)\\big)_r$, as well as $\\big(\\sum_{n\\in \\mathbb N} BMO_n(H_n^s)\\big)_r$ and $\\big(\\sum_{n\\in \\mathbb N} H^s_n(BMO_n)\\big)_r$, $1 < s < \\infty$, $1\\leq r \\leq \\infty$, are all primary.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-10-05T16:22:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B25",
      "46B07",
      "46B26",
      "30H35",
      "30H10"
    ],
    "keywords": [
      "bmo spaces",
      "finite dimensional factorization problem",
      "mixed norm hardy spaces",
      "bourgains localization method",
      "direct sum"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}