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

The equivalence of the Haar system in a rearrangement invariant space on and a sequence of pairwise disjoint functions in some Lorentz space is known to imply that up to the equivalence of norms. We show that the same holds for the class of uniform disjointly homogeneous rearrangement invariant spaces and obtain a few consequences for the properties of isomorphic embeddings of such spaces. In particular, the space with is the only uniform -disjointly homogeneous rearrangement invariant space on with nontrivial Boyd indices which has two rearrangement invariant representations on the half-axis . [ABSTRACT FROM AUTHOR]