Geodesic
On the relation between the Jackson and Jung constants of the spaces $L_ p$
Matematičeskie zametki, Tome 58 (1995) no. 6, pp. 828-836 Cet article a éte moissonné depuis la source Math-Net.Ru

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For any infinitely metrizable compact Abelian group $G$, $1\leqslant p\leqslant q<\infty$, $n\in\mathbb N$, the following relations are proved: $$ K_{pq}(G,n,G)=d_{pq}(G,n,G)=J(L_p(G),L_q(G))=\varkappa_{pq}, $$ where $K_{pq}(G,n,G)$ is the largest Jackson constant in the approximation of the system of characters by polynomials of order $n$, $d_{pq}(G,n,G)$ 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 $$ \begin{aligned} \varkappa_{pq}^q&=\sup\biggl\{\inf_c\int_0^1|f(x)-c|^q\,dx \\ &\qquad\qquad\times\biggl|\int_0^1\int_0^1|f(x)-f(y)|\biggr|^p\,dx\,dy\le1,\ f\in L_q[-1,1]\biggr\}. \end{aligned} $$ 
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     title = {On~the relation between the {Jackson} and {Jung} constants of the spaces $L_ p$},
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V. I. Ivanov. On the relation between the Jackson and Jung constants of the spaces $L_ p$. Matematičeskie zametki, Tome 58 (1995) no. 6, pp. 828-836. http://geodesic.mathdoc.fr/item/MZM_1995_58_6_a2/

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