We reformulate, modify and extend a comparison criteria of $L^{ p}$ norms obtained by Nazarov-Podkorytov and place it in the general setting of interpolation theory and majorization theory. In particular, we give norm comparison criteria for general scales of interpolation spaces, including non-commutative $L^{ p}$ and Lorentz spaces. As an application, we extend the classical Ball's integral inequality, which lies at the basis of his famous result on sections of the $n-$dimensional unit cube.
Categories: math.FA