On boundedness of integral means of Blaschke product logarithms

    YA. V. Vasylkiv Info
    A. A. Kondratyuk Info
    S. I. Tarasyuk Info

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 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 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

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September 30, 2003
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2003-09-30

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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

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