{
  "id": "0801.1745",
  "version": "v1",
  "published": "2008-01-11T10:22:26.000Z",
  "updated": "2008-01-11T10:22:26.000Z",
  "title": "On the H^1-L^1 boundedness of operators",
  "authors": [
    "S. Meda",
    "P. Sjogren",
    "M. Vallarino"
  ],
  "comment": "This paper will appear in Proceedings of the American Mathematical Society",
  "categories": [
    "math.CA"
  ],
  "abstract": "We prove that if q is in (1,\\infty), Y is a Banach space and T is a linear operator defined on the space of finite linear combinations of (1,q)-atoms in R^n which is uniformly bounded on (1,q)-atoms, then T admits a unique continuous extension to a bounded linear operator from H^1(R^n) to Y. We show that the same is true if we replace (1,q)-atoms with continuous (1,\\infty)-atoms. This is known to be false for (1,\\infty)-atoms.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-01-11T10:22:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B30",
      "46A22"
    ],
    "keywords": [
      "boundedness",
      "finite linear combinations",
      "banach space",
      "bounded linear operator",
      "unique continuous extension"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0801.1745M"
    }
  }
}