A Landau-Kolmogorov inequality for Orlicz spaces
It is shown that for the half-line \(\mathbb{R}_+\) and any Young function with corresponding Orlicz norm the Landau inequality \[ \|f^{(k)}\|^n\leq K(k, n)\|f\|^{n- k}\|f^{(n)}\|^k,\quad 0< k< n, \] holds with optimal \(K(k,n)=\) the \(K\) for the \(L^\infty\)-norm on \(\mathbb{R}_+\); the same holds for any Luxemburg norm.
scientific article; zbMATH DE number 1910306