Journal of the
Korean Mathematical Society JKMS

In this paper, we give the condition for the boundedness of the Berezin transforms on Herz spaces with a normal weight on the unit ball of $\mathbb C^n$. And we provide the integral estimates concerning pluriharmonic kernel functions. Using this, we finally obtain the growth estimates of the Berezin transforms on such Herz spaces.

Keywords: Berezin transform, Schatten space, Herz space

MSC numbers: Primary 31B10