On relationship between classes of $(\Psi, \overline\upbeta)$-differentiable functions and Gevrey classes

@article{Stepanets2009OnRB,
  title={On relationship between classes of \$(\Psi, \overline\upbeta)\$-differentiable functions and Gevrey classes},
  author={A. I. Stepanets and A. Serdyuk and A. L. Shidlich},
  journal={Ukrainian Mathematical Journal},
  year={2009},
  volume={61},
  pages={171-177}
}
We investigate the relationship between the classes of $(\Psi, \overline\upbeta)$-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 ℐα formulated in terms of their $(\Psi, \overline\upbeta)$-derivatives. 
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