On the relation between the Jackson and Jung constants of the spaces \(L_ p\)
For any infinitely metrizable compact abelian group \(G\), the following relations are proved: \[ K_{pq} (G, n, G)= d_{pq} (G, n, G)= J(L_p (G), L_q (G))= \kappa_{pq}, \] where \(K_{pq} (G,n, G)\) is the largest Jackson constant in the approximation of the system of characters is by polynomials of order \(n\), \(d_{pq} (G, n, G)\) is the best Jackson constant, \(J(L_p (G), L_q (G))= \kappa_{pq}\) is the Jung constant of the pair of real spaces \((L_p (G), L_q (G))\), and \(1\leq p\leq q< \infty\), \(n\in \mathbb{N}\).
scientific article; zbMATH DE number 921636