The best trigonometric and bilinear approximations of the functions of many variables from the classes $B_{p,θ}^r$. I - Romanyuk, A.S. (Ukrains’kyi Matematychnyi Zhurnal, 1992)
Approximations are studied of the classes $B_{p,θ}^r$of periodic functions of several variables with the help of trigonometric polynomials with a given number of harmonics. The results obtained are used to establish order estimates of the approximation of functions of the form $f(x - y)$, $f (x) \in B_{p,θ}^r$, by combinations of products of functions of a fewer number of variables.