On the membership in Bergman spaces of the derivative of a Blaschke product with zeros in a Stolz domain

It is known that the derivative of a Blaschke product whose zero sequence lies in a Stolz angle belongs to all the Bergman spaces A(P) with 0 < p < 3/2. The question of whether this result is best possible remained open. In this paper, for a large class of Blaschke products B with zeros in a Stolz angle, we obtain a number of conditions which are equivalent to the membership of B' in the space A(p) (p > 1). As a consequence, we prove that there exists a Blaschke product B with zeros on a radius such that B' is not an element of A(3/2).