On Blaschke products, Bloch functions and normal functions

D. GIRELA Y D. SUÁREZ

REVISTA MATEMATICA COMPLUTENSE

UNIV COMPLUTENSE MADRID

Año: 2011 vol. 24 p. 49 - 57

1139-1138

We prove that if G is an analytic function in the unit disc such thatG(z)→∞, as z → 1, and B is an infinite Blaschke product whose sequence ofzeros is contained in a Stolz angle with vertex at 1 then the function f = B ·G is nota normal function.We prove also some results on the asymptotic cluster set of a thin Blaschke productwith positive zeros which are related with the question of the existence of non-normalouter functions with restricted mean growth of the derivative.