Estimates of n-widths of Sobolev's classes on compact globally symmetric spaces of rank one

Estimates of Kolmogorov's and linear n-widths of Sobolev's classes on compact globally symmetric spaces of rank 1 (i.e. on Sd, Pd(R), Pd(C), Pd(H), P16(Cay)) are established. It is shown that these estimates have sharp orders in different important cases. New estimates for the (p,q)-norms of multiplier operators Λ={λk}k∈N are given. We apply our results to get sharp orders of best polynomial approximation and n-widths.