Nikol’skij-Besov classes on compact symmetric spaces of rank 1. (English. Russian original) Zbl 1011.46033

Platonov, S. S.

Dokl. Math. 55, No. 2, 266-268 (1997); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 353, No. 6, 723-725 (1997).

From the introduction: In this work, we study the Nikol’skij-Besov spaces \(B^r_{p,\theta} (M)\) for compact symmetric spaces of rank 1 so-called (CROSS) \(M\). First, we define the spaces \(B^r_{p,\theta} (M)\) in terms of averaged differences of functions along geodesics; then we obtain equivalent descriptions of these spaces with the help of the best approximations by spherical polynomials on \(M\) and provide various equivalent normalizations of these spaces. Similar results for the sphere were obtained by S. M. Nikol’skij and P. I. Lizorkin.
See also the author’s paper in Tr. Petrozavodsk. Gos. Univ. Ser. Mat. 3, 153-172 (1996; Zbl 1042.46018).

MSC:

46E35	Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
41A65	Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)

Keywords:

CROSS; Nikolskij-Besov spaces

Citations:

Zbl 1042.46018