Kolmogorov widths in the space $\widetilde L_q$ of the classes $\widetilde W_p^{\overline\alpha}$ and $\widetilde H_p^{\overline\alpha}$ of periodic functions of several variables

The author finds the order of the Kolmogorov widths $d_N(\widetilde W_p^{\overline\alpha}=\bigcap_{i=1}^m\widetilde W_p^{\alpha^i},\widetilde L_q)$ for all $1<p,q<\infty$, where $\widetilde W_p^\alpha$ is the class of periodic functions of several variables determined by a Weyl mixed fractional derivative, and $d_N(\widetilde H_p^{\overline\alpha}=\bigcap_{i=1}^m\widetilde H_p^{\alpha^i},\widetilde L_q)$ for $p\geqslant2$ or $q\geqslant2$, where $\widetilde H_p^\alpha$ is the class determined by a mixed difference.
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