Inclusion theorems for the spaces $\Cal F_{\alpha}$

Abstract

We give a new proof of one known inclusion theorem for the space $\Cal F_0$ that enables us to extend this theorem from the unit disc in $C$ to the unit ball in $C^n$, $n>1$. We also improve an inclusion relation between Bergman spaces and the spaces $\Cal F_{\alpha}$, $\alpha>0$.