Geodesic
Some remarks on level functions and their applications
Commentationes Mathematicae, Tome 56 (2016) no. 1, p. 55−86.

Voir la notice de l'article provenant de la source Annales Societatis Mathematicae Polonae Series

A comparison of the level functions considered by Halperin and Sinnamon is discussed. Moreover, connections between Lorentz-type spaces, down spaces, Cesàro spaces, and Sawyer's duality formula are explained. Applying Sinnamon's ideas, we prove the duality theorem for Orlicz−Lorentz spaces which generalizes a recent result by Kamińska, Leśnik, and Raynaud (and Nakamura). Finally, some applications of the level functions to the geometry of Orlicz−Lorentz spaces are presented.
DOI : 10.14708/cm.v56i1.1142
Classification : 46E30, 46B20, 46B42
Mots-clés : level functions, dual spaces, Orlicz−Lorentz spaces, Halperin spaces, Cesàro spaces 
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Paweł Foralewski; Karol Leśnik; Lech Maligranda. Some remarks on level functions and their applications. Commentationes Mathematicae, Tome 56 (2016) no. 1, p.  55−86. doi : 10.14708/cm.v56i1.1142. http://geodesic.mathdoc.fr/articles/10.14708/cm.v56i1.1142/

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