Estimates of Kolmogorov n-widths dn(Bpr,Lq) and linear n-widths
\da_n(B_p^r, L^q), (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 \da_n (B_p^r, L^q) were obtained by Bordin,
Kushpel, Levesley and Tozoni in a recent paper `` J. Funct. Anal. 202 (2)
(2003), 307--326''. In this paper, we obtain the sharp orders of dn(Bpr,Lq) and \da_n (B_p^r, L^q) for all the remaining (p,q). Our proof is
based on positive cubature formulas and Marcinkiewicz-Zygmund type inequalities
on CTPHS