Open AccessON BOUNDEDNESS OF INTEGRAL MEANS OF BLASCHKE PRODUCT LOGARITHMS
Author(s) -
Ya. V. Vasyl’kiv,
A. A. Kondratyuk,
S. I. Tarasyuk
Publication year - 2003
Publication title -
mathematical modelling and analysis/mathematical modeling and analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.491
H-Index - 25
eISSN - 1648-3510
pISSN - 1392-6292
DOI - 10.3846/13926292.2003.9637228
Subject(s) - blaschke product , mathematics , logarithm , product (mathematics) , combinatorics , mathematical analysis , geometry
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.