On the Membership in Bergman Spaces of the Derivative of a Blaschke Product With Zeros in a Stolz Domain

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AbstractIt is known that the derivative of a Blaschke product whose zero sequence lies in a Stolz angle belongs to all the Bergman spaces Ap 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 Ap (p < 1). As a consequence, we prove that there exists a Blaschke product B with zeros on a radius such that B′ ∉ A3/2.