Lorentz spaces for decreasing rearrangements of functions on trees

Abstract

We characterize the existence of a norm in the Lorentz spaces defined on trees, for non-linear decreasing rearrangements, as well as other functional properties (quasinormability, relationship with rearrangement invariant spaces, etc). The main tool is the characterization of the saturation in Hardy Littlewood's inequality for linearly decreasing functions.