On the Besov and Besov–Nikol'skii Classes and on Estimates for the Mixed Moduli of Smoothness of Fractional Derivatives

Fractional-order derivatives in the sense of Weyl are considered for functions of several variables. Estimates for the mixed moduli of smoothness for these derivatives are obtained in terms of the mixed moduli of smoothness of the functions themselves. These estimates are applied to study the interrelation between the Besov and Nikol'skii–Besov classes and the other classes of functions.