Journal of Mathematical Physics, Analysis, Geometry
2017, vol. 13, No 2, pp. 107-118   https://doi.org/10.15407/mag13.02.107     ( to contents , go back )
https://doi.org/10.15407/mag13.02.107

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.

Mathematics Subject Classification 2000: 30D50.
Key words: bounded analytic function, Stolz angle, Blaschke product, fractional derivative.

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