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 noncommutative 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.