On relationship between classes of (Psi, overlineupbeta)-differentiable functions and Gevrey classes

We investigate the relationship between the classes of -differentiable functions introduced by Stepanets and the well-known Gevrey classes. In particular, we establish necessary and sufficient conditions for periodic functions to belong to the Gevrey classes ℐ_α formulated in terms of their -derivatives. A. I. Stepanets (Deceased.) Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 61, No. 1, pp. 140–144, January, 2009.