Disjoint strict singularity of inclusions between rearrangement invariant spaces

Abstract

It is studied when inclusions between rearrangement invariant function spaces on the interval [0, infinity) are disjointly strictly singular operators. In particular suitable criteria, in terms of the fundamental function, for the inclusions L 1 ∩L ∞ ↪E and E↪L 1 +L ∞ to be disjointly strictly singular are shown. Applications to the classes of Lorentz and Marcinkiewicz spaces are given.