Majorization revisited: Comparison of norms in interpolation scales

Abstract

We reformulate, modify and extend a comparison criteria of Lp 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 Lp 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. © 2024 Elsevier B.V., All rights reserved.