Blaschke products with derivative in function spaces

抄録

Let B be a Blaschke product with zeros {a_n}. If B′ ∈ A^p_α for certain p and α, it is shown that Σ_n (1 - |a_n|)^β < ∞ for appropriate values of β. Also, if {a_n} is uniformly discrete and if B′ ∈ H^p or B′ ∈ A^1+p for any p ∈ (0,1), it is shown that Σ_n (1 - |a_n|)^1-p < ∞.