(FUNDAMENTAL AND APPLIED MATHEMATICS)

2000, VOLUME 6, NUMBER 1, PAGES 207-223

## About some approach to the theory of Nikolskii--Besov spaces on homogeneous manifolds

S. S. Platonov

Abstract

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 Let $M$ be a compact symmetric space of rank $1$. We have defined the Nikolskii--Besov function classes $B_{p,\theta}^r(M)$, $r > 0$, $1 \leq \theta \leq \infty$, $1 \leq p \leq \infty$, and we have obtained a constructive description of these classes in terms of the best approximations of functions $f\in L_p(M)$ by the spherical polynomials on $M$. 

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