Some remarks on level functions and their applications
Commentationes Mathematicae, Tome 56 (2016) no. 1.

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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.
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. https://geodesic-test.mathdoc.fr/item/COMA_2016__56_1_292464/