A double integral characterization of a Bergman type space and its M\'obius invariant subspace
- Resource Type
- Article
- Source
- 대한수학회보, 56(6), pp.1643-1653 Nov, 2019
- Subject
수학 - Language
- English
- ISSN
- 2234-3016
1015-8634
-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 $.