{
  "id": "0712.0492",
  "version": "v1",
  "published": "2007-12-04T11:52:56.000Z",
  "updated": "2007-12-04T11:52:56.000Z",
  "title": "Integral means and boundary limits of Dirichlet series",
  "authors": [
    "Eero Saksman",
    "Kristian Seip"
  ],
  "comment": "13 pages",
  "doi": "10.1112/blms/bdp004",
  "categories": [
    "math.CV",
    "math.FA"
  ],
  "abstract": "We study the boundary behavior of functions in the Hardy spaces HD^p for ordinary Dirichlet series. Our main result, answering a question of H. Hedenmalm, shows that the classical F. Carlson theorem on integral means does not extend to the imaginary axis for functions in HD^\\infty, i.e., for ordinary Dirichlet series in H^\\infty of the right half-plane. We discuss an important embedding problem for HD^p, the solution of which is only known when p is an even integer. Viewing HD^p as Hardy spaces of the infinite-dimensional polydisc, we also present analogues of Fatou's theorem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-12-04T11:52:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "30B50",
      "42B30",
      "46E15",
      "46J15"
    ],
    "keywords": [
      "integral means",
      "boundary limits",
      "ordinary dirichlet series",
      "hardy spaces",
      "boundary behavior"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0712.0492S"
    }
  }
}