Approximation of smooth functions on compact two-point homogeneous spaces

Estimates of Kolmogorov n-widths dn(Brp ,Lq ) and linear n-widths n(Brp,Lq ), (1 q ∞) of Sobolev’s classes Brp , (r >0, 1 p ∞) on compact two-point homogeneous spaces (CTPHS) are established. For part of (p, q) ∈ [1,∞]×[1,∞], sharporders of dn(Brp ,Lq ) or n(Brp ,Lq ) were obtained by Bordin et al. (J. Funct. Anal. 202(2) (2003) 307). In this paper, we obtain the sharporders of dn(Brp ,Lq ) and n(Brp ,Lq ) for all the remaining (p, q). Our proof is based on positive cubature formulas and Marcinkiewicz–Zygmund-type inequalities on CTPHS.