**“ Variable order fractional integrals in variable generalized Hölder spaces of holomorphic functions “**

The AMU regular meeting will take place at the YSU, faculty of Mathematics and Mechanics (room 245) on the 29th of November 2021 , 17:00.

Prof. Alexey Karapetyants from the Southern Federal University (Rostov-on Done), Russia will give a talk on the topic “ Variable order fractional integrals in variable generalized Hölder spaces of holomorphic functions “.

**Abstract:**

We introduce and study the variable generalized H\”older spaces of holomorphic functions over

the unit disc in the complex plane. These spaces are defined either directly in terms of modulus

of continuity or in terms of estimates of derivatives near the boundary. We provide conditions of

Zygmund type for imbedding of the former into the latter and vice versa. We study mapping properties of variable order fractional integrals in the frameworks of such spaces.