Some properties of embeddings of rearrangement invariant spaces

Abstract

Abstract Let and be rearrangement invariant spaces on , and let . This embedding is said to be strict if the functions in the unit ball of the space have absolutely equicontinuous norms in . For the main classes of rearrangement invariant spaces necessary and sufficient conditions are obtained for an embedding to be strict, and also the relationships this concept has with other properties of embeddings are studied, especially the property of disjoint strict singularity. In the final part of the paper, a characterization of the property of strict embedding in terms of interpolation spaces is obtained. Bibliography: 23 titles.