{
  "id": "1802.05994",
  "version": "v1",
  "published": "2018-02-16T15:55:06.000Z",
  "updated": "2018-02-16T15:55:06.000Z",
  "title": "Dimension dependence of factorization problems: bi-parameter Hardy spaces",
  "authors": [
    "Richard Lechner"
  ],
  "comment": "41 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "Given $1 \\leq p,q < \\infty$ and $n\\in\\mathbb{N}_0$, let $H_n^p(H_n^q)$ denote the canonical finite-dimensional bi-parameter dyadic Hardy space. Let $(V_n : n\\in\\mathbb{N}_0)$ denote either $\\bigl(H_n^p(H_n^q) : n\\in\\mathbb{N}_0\\bigr)$ or $\\bigl( (H_n^p(H_n^q))^* : n\\in\\mathbb{N}_0\\bigr)$. We show that the identity operator on $V_n$ factors through any operator $T : V_N\\to V_N$ which has large diagonal with respect to the Haar system, where $N$ depends \\emph{linearly} on $n$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-02-16T15:55:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B07",
      "30H10",
      "46B25",
      "60G46"
    ],
    "keywords": [
      "bi-parameter hardy spaces",
      "dimension dependence",
      "factorization problems",
      "finite-dimensional bi-parameter dyadic hardy space",
      "canonical finite-dimensional bi-parameter dyadic hardy"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 41,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}