Bilinear and trigonometric approximations of periodic functions of several variables of Besov classes Brp,θ

We obtain order-sharp estimates for bilinear approximations of periodic functions of 2d variables of the form f(x, y) = f(x - y), x, y is an element of pi(d) = Pi(d)(j=1)[-pi, pi], obtained from functions f(x) is an element of B-p(r),(theta), 1 <= p <= infinity, by translating the argument x is an element of pi(d) by vectors y is an element of pi(d). We also study the deviations of step hyperbolic Fourier sums on the classes B-1(r),(theta) and the best orthogonal trigonometric approximations in L-q 1 < q < infinity, of functions belonging to these classes.