Kolmogorov and linear widths of weighted Sobolev-type classes on a finite interval

Let I be a finite interval, r ∈ N and p(t)=dist{t,∂I}, t∈I. Denote by W^r_p,α, 0 < α < ∞, the class of functions x on I with the seminorm {double pipe};x^(r)p^α{double pipe}_Lp ≤ 1. We obtain two-sided estimates of the Kolmogorov widths d_n(W^r_p,α)_Lq and of the linear widths d_n(W^r_p,α)_Lq^lin