On the relation between the Jackson and Jung constants of the spacesL p

For any infinitely metrizable compact Abelian groupG; 1pq<,n , the following relations are proved: whereK _pq(G, n, G) is the largest Jackson constant in the approximation of the system of characters by polynomials of ordern, d _pq(G, n, G) is the best Jackson constant,J(L _p(G), L_q(G)) is the Jung constant of the pair of real spaces (L _p(G), L_q(G)), and.Translated fromMatematicheskie Zametki, Vol. 58, No. 6, pp. 828–836, December, 1995.This work was supported by the Russian Foundation for Basic Research under grant No. 95-01-00657.