Direct and Inverse Theorems on the Approximation of Functions by Fourier–Laplace Sums in the Spaces $S^{(p,q)}(\sigma^{m-1})$

In this paper, we prove direct and inverse theorems on the approximation of functions by Fourier–Laplace sums in the spaces $S^{(p,q)}(\sigma^{m-1})$, $m\ge 3$, in terms of best approximations and moduli of continuity and consider the constructive characteristics of function classes defined by the moduli of continuity of their elements. The given statements generalize the results of the author's work carried out in 2007.