Geodesic
Disjoint strict singularity of inclusions between rearrangement invariant spaces
Francisco L. Hernández 1   ; Víctor M. Sánchez 1   ; Evgueni M. Semenov 2
1 Departament of Mathematical Analysis Faculty of Mathematics Complutense University 28040 Madrid, Spain
2 Department of Mathematics Voronezh State University Voronezh 394693, Russia
Studia Mathematica, Tome 144 (2001) no. 3, pp. 209-226 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/sm144-3-2
Keywords: studied inclusions between rearrangement invariant function spaces interval infty disjointly strictly singular operators particular suitable criteria terms fundamental function inclusions cap infty hookrightarrow hookrightarrow infty disjointly strictly singular shown applications classes lorentz marcinkiewicz spaces given

Francisco L. Hernández  1   ; Víctor M. Sánchez  1   ; Evgueni M. Semenov  2

1 Departament of Mathematical Analysis Faculty of Mathematics Complutense University 28040 Madrid, Spain
2 Department of Mathematics Voronezh State University Voronezh 394693, Russia 
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Francisco L. Hernández; Víctor M. Sánchez; Evgueni M. Semenov. Disjoint strict singularity of inclusions
between rearrangement invariant spaces. Studia Mathematica, Tome 144 (2001) no. 3, pp. 209-226. doi: 10.4064/sm144-3-2

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