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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Convergence of arguments of Blaschke products in $ L\sb p$-metrics


Author: A. V. Rybkin
Journal: Proc. Amer. Math. Soc. 111 (1991), 701-708
MSC: Primary 30D50; Secondary 30E25
MathSciNet review: 1010000
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Abstract: It is shown that the naturally defined argument of a Blaschke product is a function which is the harmonic conjugate of an integrable function of constant sign. A direct construction of this function is obtained. This fact allows us to investigate the relation between conditions on the zeros of a Blaschke product and the convergence of the arguments of its partial finite subproducts in $ {L_p}$-metrics, $ 0 < p \leq \infty $.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1991-1010000-3
PII: S 0002-9939(1991)1010000-3
Keywords: Blaschke product, argument, outer function, harmonic conjugate, Hardy spaces
Article copyright: © Copyright 1991 American Mathematical Society