On Isomorphic Embeddings in the Class of Disjointly Homogeneous Rearrangement Invariant Spaces

Abstract

The equivalence of the Haar system in a rearrangementinvariant space on and a sequence of pairwise disjoint functionsin some Lorentz space is known to imply that up to the equivalence ofnorms. We show that the same holds for the class of uniformdisjointly homogeneous rearrangement invariant spaces and obtain a fewconsequences for the properties of isomorphic embeddings of such spaces.In particular, the space with is theonly uniform -disjointly homogeneous rearrangement invariant space on with nontrivial Boyd indices which has two rearrangement invariant representationson the half-axis. © 2024 Elsevier B.V., All rights reserved.