FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(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,q^r(M), $r\; >\; 0$, $1$£ q £ ¥, $1$£ p £ ¥, and we have obtained a constructive description of these classes in terms of the best approximations of functions $f$Î L_p(M) by the spherical polynomials on $M$.

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Last modified: April 11, 2000