A converse of Minkowski's type inequalities
Let \(p>0, q>0,\) and \(a_{ij}\geq 0\, (i=1,\dots,m;j=1,\dots,n)\) be real numbers. Then for \(p\geq 1\) the (converse Minkowski) inequality \[ \sum_{i=1}^m\left(\sum_{j=1}^n a_{ij}^p\right)^{1/p}\leq C\left(\sum_{j=1}^n\left(\sum_{i=1}^m a_{ij}^q\right)^{p/q}\right)^{1/p} \] holds, where \(C=C(m,n,p,q)\) is a positive constant whose dependence on its parameters is given. For \(0< p<1\) the inequality sign is reversed (and another constant is needed). Analogous integral inequalities are also obtained.
scientific article; zbMATH DE number 5823171