Estimates of the best orthogonal trigonometric approximations of the generalized multidimensional analogues of the Bernoulli kernels and classes $L^\psi_{\beta,1}$ in the space $L_q$

Abstract

We obtain order estimates of the best orthogonal trigonometric approximation of the functions $D^\psi_{\beta}$ in the space $L_q$, with $1<q<\infty$. These functions are generalized multidimensional analogs of the Bernoulli kernels. The results obtained are applied to establish a lower estimate of the best orthogonal trigonometric approximation for the classes $L^\psi_{\beta,1}$.