Approximation of smooth functions on compact two-point homogeneous spaces

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