Kolmogorov widths of an intersection of Besov classes with dominating mixed smoothness in a Besov space

Abstract

In this paper, we obtain order estimates for the Kolmogorov widths of an intersection of a finite family of Besov classes $S{B}_{p_j,{\theta }_j}^{{\overline{r}}_j}({\mathbb{T}}^d)$ with dominating mixed smoothness in a Besov space $B_{q,\sigma }^{\overline{l}}({\mathbb{T}}^d)$ in the case $2<q,\sigma <\infty$ when the parameters satisfy certain conditions of general position.