# Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty

## Disjoint strict singularity of inclusions between rearrangement invariant spaces

### Tom 144 / 2001

Studia Mathematica 144 (2001), 209-226 MSC: Primary 46E30. DOI: 10.4064/sm144-3-2

#### Streszczenie

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.

#### Autorzy

• Francisco L. HernándezDepartament of Mathematical Analysis
Faculty of Mathematics
Complutense University
e-mail
• Víctor M. SánchezDepartament of Mathematical Analysis
Faculty of Mathematics
Complutense University