A double integral characterization of a Bergman type space and its M\"obius invariant subspace
Bull. Korean Math. Soc. 2019 Vol. 56, No. 6, 1643-1653
https://doi.org/10.4134/BKMS.b190053
Published online August 6, 2019
Printed November 30, 2019
Cheng Yuan, Hong-Gang Zeng
Guangdong University of Technology; Tianjin University
Abstract : 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).
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