Disjoint strict singularity of inclusions between rearrangement invariant spaces
Volume 144 / 2001
Studia Mathematica 144 (2001), 209-226
MSC: Primary 46E30.
DOI: 10.4064/sm144-3-2
Abstract
It is studied when inclusions between rearrangement invariant function spaces on the interval $[0,\infty )$ are disjointly strictly singular operators. In particular suitable criteria, in terms of the fundamental function, for the inclusions $L^1\cap L^\infty \hookrightarrow E$ and $E\hookrightarrow L^1+L^\infty $ to be disjointly strictly singular are shown. Applications to the classes of Lorentz and Marcinkiewicz spaces are given.
