Convergence of arguments of Blaschke products in 𝐿_{𝑝}-metrics

Rybkin, A. V.

doi:10.1090/S0002-9939-1991-1010000-3

Convergence of arguments of Blaschke products in $L_ p$-metrics
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by A. V. Rybkin PDF

Proc. Amer. Math. Soc. 111 (1991), 701-708 Request permission

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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