Approximation of Sobolev-type classes with quasi-seminorms (Q2566502)

Let be given a positive integer \(r\) and \(0< p< 1\). The authors deal with the Kolmogorov \(n\)-width, the linear \(n\)-width and the pseudo-dimensional \(n\)-width of two Sobolev type classes \(W^r_{p,\infty}\) and \(V^r_p\) in the \(L_q\)-norm. It is proved that in the case of \(W^r_{p,\infty}\) these three widths are for any \(0< q\leq\infty\) asymptotically 1 and that in the case of \(V^r_p\) they are asymptotically \(n^{-r}\) when \(0< q< 1\).