Geodesic
On some equivalent geometric properties in the Besicovitch-Orlicz space of almost periodic functions with Luxemburg norm
Commentationes Mathematicae Universitatis Carolinae, Tome 51 (2010) no. 1, pp. 25-35 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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The paper is concerned with the characterization and comparison of some local geometric properties of the Besicovitch-Orlicz space of almost periodic functions. Namely, it is shown that local uniform convexity, $H$-property and strict convexity are all equivalent. In our approach, we first prove some metric type properties for the modular function associated to our space. These are then used to prove our main equivalence result.
The paper is concerned with the characterization and comparison of some local geometric properties of the Besicovitch-Orlicz space of almost periodic functions. Namely, it is shown that local uniform convexity, $H$-property and strict convexity are all equivalent. In our approach, we first prove some metric type properties for the modular function associated to our space. These are then used to prove our main equivalence result.
Classification : 42A75, 46B20
Keywords: locally uniform convexity; strict convexity; $H$-property; Besicovitch-Orlicz space; almost periodic functions 
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     title = {On some equivalent geometric properties in the {Besicovitch-Orlicz} space of almost periodic functions with {Luxemburg} norm},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
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     zbl = {1224.46018},
     language = {en},
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Bedouhene, Fazia; Morsli, Mohamed; Smaali, Mannal. On some equivalent geometric properties in the Besicovitch-Orlicz space of almost periodic functions with Luxemburg norm. Commentationes Mathematicae Universitatis Carolinae, Tome 51 (2010) no. 1, pp. 25-35. http://geodesic.mathdoc.fr/item/CMUC_2010_51_1_a3/