Relation between moduli of smoothness and partial sums of Fourier series and embedding theorems for Nikol'skii classes (Q656310)

It is well-known that there is an intimate connection between the modulus of continuity of a function and the size of the remainder term of the partial sums of its Fourier series. In previous work, B. V. Simonov proved that a similar relation holds for the modulus of smoothness of any positive order, see [\textit{M. K. Potapov} and \textit{B. V. Simonov}, ``On the interrelation of the generalized Besov-Nikol'skii and Weyl-Nikol'skii classes of functions'', Anal. Math. 22, No. 4, 299--316 (1996; Zbl 0892.46029)]. In the paper under review an analogous result is proved in the case of mixed moduli of smoothness in a mixed metric.