Kolmogorov and linear widths of weighted Besov classes

We study the Kolmogorov m-widths and the linear m-widths of the weighted Besov classes on −1,1], where Lq,μ, 1?q?∞, denotes the Lq space on −1,1] with respect to the measure , μ>0. Optimal asymptotic orders of and as m→∞ are obtained for all 1?p,τ?∞. It turns out that in many cases, the orders of are significantly smaller than the corresponding orders of the best m-term approximation by ultraspherical polynomials, which is somewhat surprising.