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 that
then 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 eilučių metodu gauta analitinių funkcijų Blaschke sandaugos logaritmų integralinių reikšmių elgsenos charakteristika. Jeigu Blaschke sandaugos B nulių funkcija n(r, B) tenkina sąlygą [], čia l yra neneigiama funkcija intervale (0,1) ir [
], tuomet q‐integralinė reikšmė [
] yra aprėžta intervale (0,1), kai log B yra B logaritmo šaka.
First Published Online: 14 Oct 2010
Keywords:
Fourier series, anlytic functions, Blaschke product logarithmsHow to Cite
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Copyright (c) 2003 The Author(s). Published by Vilnius Gediminas Technical University.
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Copyright (c) 2003 The Author(s). Published by Vilnius Gediminas Technical University.
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This work is licensed under a Creative Commons Attribution 4.0 International License.