The work was published in:
Mat. Zametki 60 (1996), no. 3, pp. 333-355;

English translation: Math. Notes. 60 (1996), no. 3, pp. 248-263.

English translation: Math. Notes. 60 (1996), no. 3, pp. 248-263.

S U M M A R Y

41A17 41A44

B a b e n k o A. G.

**Exact Jackson-Stechkin type inequality in space of functions
on the multidimensional sphere.**

In this paper we prove Jackson-Stechkin type inequality
which is exact for every here is the best approximation of the function by spherical polynomials of degree is the th modulus of continuity of based on translation

is the measure of the unit Euclidean sphere is the first positive zero of the Gegenbauer's cosine polynomial .