Two properties of Bloch functions (Q2706759)

A holomorphic function \(f\) in the unit disk \(D\) is called a Bloch function if NEWLINE\[NEWLINE\limsup_{|z|\to 1}(1-|z|^2)|f'(z)|<+\infty.NEWLINE\]NEWLINE A family \(F\) of holomorphic functions on \(D\), is said to be a strong analytic normal family in \(D\), if every sequence \({f_n} \subset F\) contains a subsequence \({f_{n_k}}\) which converges to a holomorphic function uniformly on compact subsets of \(D\). In term of a strong analytic normal family, the author gives a characteristic property of a Bloch function and a sufficient condition for a Bloch function to be bounded on boundary angles.