Sharp Orders of n-Widths of Sobolev's Classes on Compact Globally Symmetric Spaces of Rank 1

Sharp orders of Kolmogorov's $n$-widths $d_{n}(W^{r}_{p}(M^{d}),{\}L_{q}(M^{d}))$ of Sobolev's classes $W^{r}_{p}(M^{d})$ on compact globally symmetric spaces of rank 1 are found for different $p$ and $q$. In particular, we are considering the cases $1 \leq p \leq 2 \leq q < \infty$, $2 \leq p \leq q < \infty$ and $1 < q \leq p \leq 2$.