Geodesic
Integral Means and Zero Distributions of Blaschke Products
Canadian journal of mathematics, Tome 24 (1972) no. 5, pp. 755-760

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A sequence {zn} in D = {z: |z| < 1} is a Blaschke sequence if and only if If 0 appears m times in {zn} then is the Blaschke product defined by {zn}. The set of all Blaschke products will be denoted by . If B ∊ it is well-known that B is regular in D, and |B(z, {zn})| < 1 when z ∊ D.For a given pair of values p in (0, ∞) and q in [0, ∞) we denote by I(p, g) the class of all Blaschke products B(z, {zn}) such that as r → 1 — 0. In the case q ≦ max(p — 1,0) the classes of functions B and I(p, q) are identical: this is a particular case of an elementary theorem for functions subharmonic in a disc, the analogous theorem for functions subharmonic in a half-plane appearing in [1], 
Linden, C. N. Integral Means and Zero Distributions of Blaschke Products. Canadian journal of mathematics, Tome 24 (1972) no. 5, pp. 755-760. doi: 10.4153/CJM-1972-072-x
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[1] 1. Flett, T. M., On the rate of growth of mean values of holomorphic and harmonic functions, Proc. London Math. Soc. 20 (1970), 749–768. Google Scholar

[2] 2. MacLane, G. R. and Rubel, L. A., On the growth of Blaschke products, Can. J. Math. 21 (1969), 595–601. Google Scholar

[3] 3. Linden, C. N., On Blaschke products of restricted growth, Pacific J. Math. 38 (1971), 501–513. Google Scholar

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