On Boundedness of Integral Means of Blaschke Product Logarithms

Abstract

Using the Fourier series method for the analytic functions, we obtain a result characterizing the behaviour of the integral means of Blaschke product logarithms. Namely, if the zero counting function n(r, B) of the Blaschke product B satisfies the conditionwhere l is a positive function on (0, 1) such thatthen the q‐integral mean mq (r, log B) = [] is bounded on (0,1), where log B is a branch of the logarithm of B. Šiame straipsnyje Furje eilučiu metodu gauta analitiniu funkciju Blaschke sandaugos logaritmu integraliniu reikšmiu elgsenos charakteristika. Jeigu Blaschke sandaugos B nuliu funkcija n(r, B) tenkina salyga [], čia l yra neneigiama funkcija intervale (0,1) ir [], tuomet q‐integraline reikšme [] yra aprežta intervale (0,1), kai log B yra B logaritmo šaka.