Bulletin of the
Korean Mathematical Society BKMS

This paper shows that if $1-1-\frac{p}{2} $ and $f$ is holomorphic on the unit ball $\bbn$, then $$\ibn |Rf(z)|^p(1-|z|^2)^{p+\alpha} \rd v_\alpha(z)<\infty$$ if and only if $$\ibn\ibn\frac{|f(z)-f(w)|^p}{|1-\langle z,w\rangle|^{n+1+s+t-\alpha}} (1-|w|^2)^s(1-|z|^2)^t \rd v(z)\rd v(w)<\infty,$$ where $s,t>-1$ with $\min(s,t)>\alpha $.

Keywords: Bergman space, $Q_p$ spaces

MSC numbers: Primary 30H25, 32A36

Supported by: Cheng Yuan is supported by the National Natural Science Foundation of China (Grant Nos. 11501415).
Hong-Gang Zeng is supported by the National Natural Science Foundation of China (Grant Nos. 11301373).