Hyperbolic mean growth of bounded holomorphic functions in the ball
Hyperbolic mean growth of bounded holomorphic functions in the ball
We consider the hyperbolic Hardy class $\varrho H^{p}(B)$, $0<p<\infty$. It consists of $\phi$ holomorphic in the unit complex ball $B$ for which $\vert \phi \vert < 1$ and \begin{equation*}\sup _{0<r<1} \int _{\partial B} \left \{ \varrho (\phi (r\zeta ), 0)\right \}^{p} d\sigma (\zeta ) ~<~ \infty ,\end{equation*} where $\varrho$ denotes …