Kolmogorov widths of the classes $L_{\beta, p}^\psi$ of periodic functions in the space $L_q$

Abstract

We find the exact order estimates of the Kolmogorov widths of the classes $L_{\beta, p}^\psi$ in the space $L_q$ for some relations between the parameters $p$ and $q$ and certain limitations on the rate of decrease of the function $\psi$.