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Journal of Function Spaces and Applications
Volume 6 (2008), Issue 3, Pages 277-292
http://dx.doi.org/10.1155/2008/107568

A criterion of weak compactness for operators on subspaces of Orlicz spaces

1Université d'Artois, Laboratoire de Mathématiques de Lens EA 2462, Fédération CNRS Nord-Pas-de-Calais FR 2956, Faculté des Sciences Jean Perrin, Rue Jean Souvraz, S.P.18, 62 307 LENS Cedex, France
2Université des Sciences et Technologies de Lille, Laboratoire Paul Painlevé U.M.R. CNRS 8524, U.F.R. de Mathématiques, 59 655 VILLENEUVE D'ASCQ Cedex, France
3Universidad de Sevilla, Facultad de Matemáticas, Dpto de Análisis Matemático, Apartado de Correos 1160, 41 080 SEVILLA, Spain

Received 1 September 2007

Academic Editor: Nigel Kalton

Copyright © 2008 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We give a criterion of weak compactness for the operators on the Morse-Transue space MΨ, the subspace of the Orlicz space LΨ generated by L.