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About some approach to the theory of Nikolski\v{i}–Besov spaces on homogeneous manifolds

S. S. Platonov

Petrozavodsk State University

Abstract: Let $M$ be a compact symmetric space of rank 1. We have defined the Nikolski\v{i}–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 $M$.

UDC: 517.518

Received: 01.02.1996

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