Интегральные средние производных локально однолистных функций Блоха

V. V. Starkov

Problemy analiza, no. 7 (2000), pp. 83-105.

Résumé

In this paper we give examples of locally univalent Bloch functions $f_{k}, (k=0,1,2,\dots )$, such that for $p\ge 1/2$ the integral means $I_{p} (r,f')=\frac{1}{2\pi}\int\limits_{0}^{2\pi}|f'(re^{i\theta})|^{p}d\theta, p\ge 1/2, r\in [0,1)$, behave like $c_{k}(1-r)^{1/2-p}(-log(1-r))^{k}$ for $r\to 1^{-}$.