Mean growth of the derivative of a Blaschke product

抄録

If B is a Blaschke product with zeros {a_n} and if ∑_n(1−|a_n|)^α is finite for some α∈(1/2, 1], then limits are found on the rate of growth of ∫₀^2π|B'(re^it)|^p dt in agreement with a known result for a α∈(0, 1/2). Also, a converse is established in the case of an interpolating Blaschke product whenever 0<α<1.