On the relation between the Lebesgue integral means and Nevanlinna characteristic of analytic functions in the unit disc

Author Ya. V. Vasyl’kiv, O. Z. Korenivs’ka
YaVVasylkiv@gmail.com, korenivskaolena@rambler.ru
Lviv National University

Abstract The best possible asymptotic estimates for Lebesgue integral means $m_{p}(r,\log f), 1 \leq p$ of logarithms of analytic functions $f(z)$ in the unit disc in terms of their Nevanlinna characteristic $T(r,f)$ are obtained. We get sharp relation between the order of $T(r,f)$ and the order of $m_{p}(r,\log f)$ for an analytic function $f(z)$ of finite order $\alpha(f).$ This generalizes well-known results of L.~R.~Sons and C.~N.~Linden.
Keywords Nevanlinna characteristic; analytic functions in the unit disc
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Pages 58-64
Volume 36
Issue 1
Year 2011
Journal Matematychni Studii
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