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# A Characterization of Bergman Spaces on the Unit Ball of ${\mathbb C}^n$. II

Published:2011-03-23
Printed: Mar 2012
• Songxiao Li,
Department of Mathematics, Jiaying University, Meizhou, Guangdong 514015, China
• Hasi Wulan,
Department of Mathematics, Shantou University, Shantou, Guangdong 515063, China
• Kehe Zhu,
Department of Mathematics and Statistics, State University of New York, Albany, NY 12222, USA
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## Abstract

It has been shown that a holomorphic function $f$ in the unit ball $\mathbb{B}_n$ of ${\mathbb C}_n$ belongs to the weighted Bergman space $A^p_\alpha$, $p>n+1+\alpha$, if and only if the function $|f(z)-f(w)|/|1-\langle z,w\rangle|$ is in $L^p(\mathbb{B}_n\times\mathbb{B}_n,dv_\beta \times dv_\beta)$, where $\beta=(p+\alpha-n-1)/2$ and $dv_\beta(z)= (1-|z|^2)^\beta\,dv(z)$. In this paper we consider the range $0n+1+\alpha$ is particularly interesting.
 Keywords: Bergman spaces, unit ball, volume measure
 MSC Classifications: 32A36 - Bergman spaces