{
  "id": "1908.06458",
  "version": "v1",
  "published": "2019-08-18T15:13:01.000Z",
  "updated": "2019-08-18T15:13:01.000Z",
  "title": "Riesz means in Hardy spaces on Dirichlet groups",
  "authors": [
    "Andreas Defant",
    "Ingo Schoolmann"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "Given a frequency $\\lambda=(\\lambda_n)$, we study when almost all vertical limits of a $\\mathcal{H}_1$-Dirichlet series $\\sum a_n e^{-\\lambda_ns}$ are Riesz-summable almost everywhere on the imaginary axis. Equivalently, this means to investigate almost everywhere convergence of Fourier series of $H_1$-functions on so-called $\\lambda$-Dirichlet groups, and as our main technical tool we need to invent a weak-type $(1, \\infty)$ Hardy-Littlewood maximal operator for such groups. Applications are given to $H_1$-functions on the infinite dimensional torus $\\mathbb{T}^\\infty$, ordinary Dirichlet series $\\sum a_n n^{-s}$, as well as bounded and holomorphic functions on the open right half plane, which are uniformly almost periodic on every vertical line.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-08-18T15:13:01.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "dirichlet groups",
      "riesz means",
      "hardy spaces",
      "open right half plane",
      "ordinary dirichlet series"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}