Linear widths of Hölder–Nikol'skii classes of periodic functions of several variables

We consider the linear widths $\lambda_N\bigl(W_p^r(T^n),L_q\bigr)$ and $\lambda_N\bigl(H_p^r(T^n),L_q\bigr)$ of the classes $W_p^r(T^n)$ and $H_p^r(T^n)$ of periodic functions of one or several variables in the space $L_q$. For the Sobolev classes $W_p^r(T^n)$ of functions of one or several variables, we state some well-known results without proof; for the Hölder–Nikol'skii classes $H_p^r(T^n)$, we state some well-known results, prove some new results, and present some previously unpublished proofs.