{
  "id": "1512.01452",
  "version": "v1",
  "published": "2015-12-03T14:37:12.000Z",
  "updated": "2015-12-03T14:37:12.000Z",
  "title": "On some spaces of holomorphic functions of exponential growth on a half-plane",
  "authors": [
    "Marco M. Peloso",
    "Maura Salvatori"
  ],
  "categories": [
    "math.CV",
    "math.FA"
  ],
  "abstract": "In this paper we study spaces of holomorphic functions on the right half-plane $\\cal R$, that we denote by $\\cal M^p_\\omega$, whose growth conditions are given in terms of a translation invariant measure $\\omega$ on the closed half-plane $\\overline\\cal R$. Such a measure has the form $\\omega=\\nu\\otimes m$, where $m$ is the Lebesgue measure on $\\mathbb R$ and $\\nu$ is a regular Borel measure on $[0,+\\infty)$. We call these spaces generalized Hardy-Bergman spaces on the half-plane $\\cal R$. We study in particular the case of $\\nu$ purely atomic, with point masses on an arithmetic progression on $[0,+\\infty)$. We obtain a Paley-Wiener theorem for $\\cal M^2_\\omega$, and consequentely the expression for its reproducing kernel. We study the growth of functions in such space and in particular show that $\\cal M^p_\\omega$ contains functions of order 1. Moreover, we prove that the orthogonal projection from $L^p(\\cal R,d\\omega)$ into $\\cal M^p_\\omega$ is unbounded for $p\\neq2$. Furthermore, we compare the spaces $\\cal M^p_\\omega$ with the classical Hardy and Bergman spaces, and some other Hardy-Bergman-type spaces introduced more recently.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-12-03T14:37:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "30H99",
      "46E22",
      "30C15",
      "30C40"
    ],
    "keywords": [
      "holomorphic functions",
      "exponential growth",
      "spaces generalized hardy-bergman spaces",
      "regular borel measure",
      "translation invariant measure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151201452P"
    }
  }
}