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

Open Access article
 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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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 Bergman spaces, unit ball, volume measure
MSC Classifications: 32A36 show english descriptions Bergman spaces 32A36 - Bergman spaces

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