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 A double integral characterization of a Bergman type space and its Mobius invariant subspace Bull. Korean Math. Soc.Published online August 6, 2019 Cheng Yuan and Hong-Gang Zeng School of Applied Mathematics, Guangdong University of Technology, School of Mathematics, Tianjin University Abstract : This paper shows that if $1-1-\frac{p}{2}$ and $f$ is holomorphic on the unit ball $\mathbb{B}_n$, then $$\int_{\mathbb{B}_n} |Rf(z)|^p(1-|z|^2)^{p+\alpha} \mathrm{d} v_\alpha(z)<\infty$$ if and only if $$\int_{\mathbb{B}_n}\int_{\mathbb{B}_n}\frac{|f(z)-f(w)|^p}{|1-\langle z,w\rangle|^{n+1+s+t-\alpha}} (1-|w|^2)^s(1-|z|^2)^t \mathrm{d} v(z)\mathrm{d} v(w)<\infty,$$ where $s,t>-1$ with $\min(s,t)>\alpha$. Keywords : Bergman space, $Q_p$ spaces MSC numbers : 30H25, 32A36 Full-Text :