{
  "id": "0809.1719",
  "version": "v4",
  "published": "2008-09-10T07:12:11.000Z",
  "updated": "2012-06-20T15:26:28.000Z",
  "title": "Duality in spaces of finite linear combinations of atoms",
  "authors": [
    "Fulvio Ricci",
    "Joan Verdera"
  ],
  "comment": "The paper has appeared as Ricci, F., & Verdera, J. (2011). Duality in spaces of finite linear combinations of atoms. Transactions of the American Mathematical Society, 363(3), 1311-1323",
  "categories": [
    "math.FA"
  ],
  "abstract": "In this note we describe the dual and the completion of the space of finite linear combinations of $(p,\\infty)$-atoms, $0<p\\leq 1$ on ${\\mathbb R}^n$. As an application, we show an extension result for operators uniformly bounded on $(p,\\infty)$-atoms, $0<p < 1$, whose analogue for $p=1$ is known to be false. Let $0 < p <1$ and let $T$ be a linear operator defined on the space of finite linear combinations of $(p,\\infty)$-atoms, $0<p < 1 $, which takes values in a Banach space $B$. If $T$ is uniformly bounded on $(p,\\infty)$-atoms, then $T$ extends to a bounded operator from $H^p({\\mathbb R}^n)$ into $B$.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2012-06-20T15:26:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B30"
    ],
    "keywords": [
      "finite linear combinations",
      "banach space",
      "extension result",
      "completion"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0809.1719R"
    }
  }
}