Approximation of Classes of Periodic Functions in Several Variables

We study the approximation of the classes $B_{p,\theta }^r$ and $W_{p,\alpha }^r$ of periodic functions of several variables by multiple Fourier sums of fixed order constructed with regard to individual properties of functions from these classes. In a number of cases, such approximations allow us to achieve a better degree of approximation of the classes indicated above as compared to their approximation by staircase hyperbolic Fourier sums.