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 Bp,qr(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 Lp(M) by the spherical polynomials on M.


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