Widths of weighted Sobolev classes on the ball

We study the Kolmogorov nn-widths dn(BWp,μr,Lq,μ) and the linear nn-widths δn(BWp,μr,Lq,μ) of weighted Sobolev classes BWp,μr on the unit ball BdBd in Lq,μLq,μ, where Lq,μLq,μ, 1≤q≤∞1≤q≤∞, denotes the weighted LqLq space of functions on BdBd with respect to weight (1−|x|2)μ−12,μ≥0. Optimal asymptotic orders of dn(BWp,μr,Lq,μ) and δn(BWp,μr,Lq,μ) as n→∞n→∞ are obtained for all 1≤p,q≤∞1≤p,q≤∞ and μ≥0μ≥0.