Angular and Tangential Limits of Blaschke Products and their Successive Derivatives

Abstract

In this paper, we shall be concerned with bounded, holomorphic functions of the form where (1) (2) and (3) B(z{a n }) is called a Blaschke product , and any sequence {a n } which satisfies (2) and (3) is called a Blaschke sequence . For a general discussion of the properties of Blaschke products, see (18, pp. 271-285) or (14, pp. 49-52). According to a theorem due to Riesz (15), a Blaschke product has radial limits of modulus one almost everywhere on C = {z: |z| = 1}. Moreover, it is common knowledge that, if a Blaschke product has a radial limit at a point, then it also has an angular limit at the point (see 14, p. 19 and 6, p. 457).