Nonlinear approximation of the classes $F_{q,r}^{\psi}$ of functions of several variables in the integral metrics

Abstract

In the paper, exact order estimates of nonlinear approximative characteristics (such as the best $m$-member of the trigonometric approximation, better than the $m$-th term of the orthogonal trigonometric approximation, approximation of the $m$-member of the grid by polynomials) are found in the class $ℱ_{q,r}^{\psi}$ of functions of several variables in the integral metric.