Abstract
Order estimates for the Kolmogorov \(n\) -widths of the intersection of any family of balls \(\nu_\alpha B^{\overline{k}}_{\overline{p}_\alpha}\) in the space \(l_q^k\) for \(1\le q\le 2\) and \(n\le k/2\) are obtained; here \(\overline{p}_\alpha=(p_{\alpha,1}, \dots, p_{\alpha,d})\) , \(\overline{k}=(k_1, \dots, k_d)\) , \(k=k_1\dots k_d\) , and \(B^{\overline{k}}_{\overline{p}_\alpha}\) is the unit ball with respect to the anisotropic norm determined by the vector \(\overline{p}_\alpha\) .
