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Atomic decomposition and weak factorization for Bergman–Orlicz spaces

Volume 160 / 2020

David Békollé, Aline Bonami, Edgar Tchoundja Colloquium Mathematicum 160 (2020), 223-245 MSC: Primary 47B35; Secondary 32A35, 32A37. DOI: 10.4064/cm7597-3-2019 Published online: 31 January 2020

Abstract

For $\mathbb B^n$ the unit ball of $\mathbb C^n$, we consider Bergman–Orlicz spaces of holomorphic functions in $L^\Phi _\alpha (\mathbb B^n)$, which are generalizations of classical Bergman spaces. We obtain atomic decomposition for functions in the Bergman–Orlicz space $\mathcal A^\Phi _\alpha (\mathbb B^n)$ where $\Phi $ is either a convex or a concave growth function. We then prove weak factorization theorems involving the Bloch space and a Bergman–Orlicz space, and also weak factorization theorems involving two Bergman–Orlicz spaces.

Authors

  • David BékolléDepartment of Mathematics
    Faculty of Science
    University of Ngaoundere
    P.O. Box 484, Ngaoundere, Cameroon
    e-mail
  • Aline BonamiFédération Denis Poisson
    MAPMO CNRS-UMR 7349
    Université d’Orléans
    45067 Orléans Cedex 2, France
    e-mail
  • Edgar TchoundjaDepartment of Mathematics
    Faculty of Science
    University of Yaoundé I
    P.O. Box 812, Yaoundé, Cameroon
    and
    Department of Mathematics
    Washington University in St. Louis
    One Brookings Drive
    St. Louis, MO 63130, U.S.A.
    e-mail
    e-mail

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