Asymptotic Behavior of Fractional Derivatives of Bounded Analytic Functions

I. Chyzhykov and Yu. Kosaniak

Faculty of Mechanics and Mathematics, Lviv Ivan Franko National University
1 Universytetska Str., Lviv 79000, Ukraine
E-mail: chyzhykov@yahoo.com yulia kosaniak@ukr.net

Received December 20, 2015, revised October 29, 2016

Abstract

We find sharp sufficient conditions for the boundedness of fractional
derivatives of a bounded analytic function in a Stolz angle. If F ≠ 0 in
the unit disc, the necessary and sufficient conditions for the boundedness of fractional derivatives of its argument in a Stolz angle are established.