The average widths and non-linear widths of the classes of multivariate functions with bounded moduli of smoothness. (Q1566063)

The authors estimate the average linear \(\sigma\)-width, the average Kolmogorov \(\sigma\)-width and the average Bernstein \(\sigma\)-width of certain classes of functions belonging to \(L_{{\mathbf p}}(\mathbb R^d)\) \(({\mathbf p}\in [1,\infty)^d)\) and to \(L_{pq}(\mathbb R^d)\) \((p,q\in [1,\infty))\), respectively, with bounded moduli of smoothness.