Majorization revisited: Comparison of norms in interpolation scales

Sergey V. Astashkin, Konstantin V. Lykov, Mario Milman

Published 2021-07-25Version 1

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.