Angular and Tangential Limits of Blaschke Products and their Successive Derivatives
G. T. Cargo
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Source: Crossref
Published: Jan 1, 1962
DOI: 10.4153/cjm-1962-026-2
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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).
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