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Weighted composition operators from Zygmund spaces to Bloch spaces on the unit ball

Volume 114 / 2015

Yu-Xia Liang, Chang-Jin Wang, Ze-Hua Zhou Annales Polonici Mathematici 114 (2015), 101-114 MSC: Primary 47B38; Secondary 32A37, 32A38, 32H02, 47B33. DOI: 10.4064/ap114-2-1

Abstract

Let $H(\mathbb {B})$ denote the space of all holomorphic functions on the unit ball $\mathbb {B}\subset \mathbb {C}^n.$ Let $\varphi $ be a holomorphic self-map of $\mathbb {B}$ and $u\in H(\mathbb {B})$. The weighted composition operator $uC_\varphi $ on $H(\mathbb {B})$ is defined by $$ uC_\varphi f(z)=u(z) f(\varphi (z)). $$ We investigate the boundedness and compactness of $uC_\varphi $ induced by $u$ and $\varphi $ acting from Zygmund spaces to Bloch (or little Bloch) spaces in the unit ball.

Authors

  • Yu-Xia LiangSchool of Mathematical Sciences
    Tianjin Normal University
    Tianjin 300387, P.R. China
    e-mail
  • Chang-Jin WangSchool of Science
    Jimei University
    Xiamen, Fujian 361021, P.R. China
    e-mail
  • Ze-Hua ZhouDepartment of Mathematics
    Tianjin University
    Tianjin 300072, P.R. China
    and
    Center for Applied Mathematics
    Tianjin University
    Tianjin 300072, P.R. China
    e-mail
    e-mail

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