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1. CMB 2011 (vol 55 pp. 146)

Li, Songxiao; Wulan, Hasi; Zhu, Kehe
A Characterization of Bergman Spaces on the Unit Ball of ${\mathbb C}^n$. II
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
Category:32A36

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