Widths of the Besov Classes $B_{p,\theta}^r(\mathbb T^d)$

In this paper we obtain estimates of the orders of Kolmogorov widths of the Besov classes $B_{p,\theta}^r(\mathbb T^d)$ of periodic functions of several variables with dominant mixed derivative (defined in the sense of Weyl) in the space $L_q$, $r\in\mathbb R^d$, $1<p,q<\infty$, $0<\theta\le\infty$. The proposed approach to calculating widths can also be used for finding the widths of the Sobolev classes $W_p^r(\mathbb T^d)$ (by embedding them in the Besov classes $B_{p,\theta}^r(\mathbb T^d)$) as well as for calculating some other widths (such as Alexandroff, linear, projective, and orthoprojective widths).