MAJORIZATION BY L^p-NORMS

Our primary objective is to develop sufficient conditions for a non­negative rearrangeable real map f to have a larger L^p-norm than another such function g, for every p ≥ 1. To this end, we first extend some well-known mar jorization type integral inequalities to the context of an arbitrary measure space. Then, we prove that if both f and g are bounded below by 1, and if the entropy of the decreasing rearrangement of f supermajorizes that of g, then ‖f‖_LP ≥ ‖g‖_LP holds for every p ≥ 1. We also consider some generalizations of this fact, as well as a basic application to quantum information theory.