Share:


On boundedness of integral means of Blaschke product logarithms

    YA. V. Vasylkiv Affiliation
    ; A. A. Kondratyuk Affiliation
    ; S. I. Tarasyuk Affiliation

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.


First Published Online: 14 Oct 2010

Keyword : Fourier series, anlytic functions, Blaschke product logarithms

How to Cite
Vasylkiv, Y. V., Kondratyuk, A. A., & Tarasyuk, S. I. (2003). On boundedness of integral means of Blaschke product logarithms. Mathematical Modelling and Analysis, 8(3), 259-265. https://doi.org/10.3846/13926292.2003.9637228
Published in Issue
Sep 30, 2003
Abstract Views
116
PDF Downloads
60