Best trigonometric and bilinear approximations for the classes of $(ψ, β)$ -differentiable periodic functions

Abstract

We establish the exact-order estimates for the best $m$-term trigonometric approximations of the classes $L^{\psi}_{\beta, 1}$ in the space $L_q,\; 2 < q < \infty$. We also determine the exact orders of the best bilinear approximations for the classes of functions of two variables generated by functions of a single variable from the class$L^{\psi}_{\beta, p}$ by the shifts of the argument in the space $L_{q_1,q_2},\; 1 \leq q_1,\; q_2 \leq \infty$.