Linear and Kolmogorov widths of the classes B^{\Omega}_{p, \theta} of periodic functions of one and several variables

Abstract

Some estimates exact in order for linear widths of the classes $B^{\Omega}_{p, \theta}$ of periodic multivariable functions in the space $L_q$ with certain relations between the parameters $p$, $q,$ and $\theta$ are obtained. In the univariate case, the estimates exact in order for Kolmogorov and linear widths of the classes $B^{\omega}_{\infty, \theta}$ in the space $L_q$, $1 \leq q \leq \infty,$ are established.