On some equivalent geometric properties in the Besicovitch-Orlicz space of almost periodic functions with Luxemburg norm
Fazia Bedouhene; Mohamed Morsli; Mannal Smaali
Commentationes Mathematicae Universitatis Carolinae (2010)
- Volume: 51, Issue: 1, page 25-35
- ISSN: 0010-2628
Access Full Article
topAbstract
topHow to cite
topBedouhene, Fazia, Morsli, Mohamed, and Smaali, Mannal. "On some equivalent geometric properties in the Besicovitch-Orlicz space of almost periodic functions with Luxemburg norm." Commentationes Mathematicae Universitatis Carolinae 51.1 (2010): 25-35. <http://eudml.org/doc/37742>.
@article{Bedouhene2010,
abstract = {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.},
author = {Bedouhene, Fazia, Morsli, Mohamed, Smaali, Mannal},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {locally uniform convexity; strict convexity; $H$-property; Besicovitch-Orlicz space; almost periodic functions; locally uniform convexity; strict convexity; -property; Besicovitch-Orlicz space; almost periodic function},
language = {eng},
number = {1},
pages = {25-35},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On some equivalent geometric properties in the Besicovitch-Orlicz space of almost periodic functions with Luxemburg norm},
url = {http://eudml.org/doc/37742},
volume = {51},
year = {2010},
}
TY - JOUR
AU - Bedouhene, Fazia
AU - Morsli, Mohamed
AU - Smaali, Mannal
TI - On some equivalent geometric properties in the Besicovitch-Orlicz space of almost periodic functions with Luxemburg norm
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2010
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 51
IS - 1
SP - 25
EP - 35
AB - 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.
LA - eng
KW - locally uniform convexity; strict convexity; $H$-property; Besicovitch-Orlicz space; almost periodic functions; locally uniform convexity; strict convexity; -property; Besicovitch-Orlicz space; almost periodic function
UR - http://eudml.org/doc/37742
ER -
References
top- Besicovitch A.S., Almost Periodic Functions, Dover Publications, Inc., New York, 1955. Zbl0065.07102MR0068029
- Bedouhene F., Morsli M., On the strict convexity of the Weyl-Orlicz space of almost periodic functions, Comment. Math. Prace Mat. 40 (2000), 33–47. MR1810383
- Chen S., Geometry of Orlicz spaces, Dissertationes Math. 356 (1996). Zbl1089.46500MR1410390
- Cui Y.A., Hudzik H., Meng C., 10.1023/A:1006533011548, Acta Math. Hungar. 80 (1998), no. 1–2, 143–154. MR1624558DOI10.1023/A:1006533011548
- Hillmann T.R., Besicovitch-Orlicz spaces of almost periodic functions, Real and Stochastic Analysis, Wiley, New York, 1986, pp. 119–167. Zbl0656.46020MR0856581
- Hudzik H., Kurk W., Wisla M., 10.1006/jmaa.1995.1043, J. Math. Anal. Appl. 189 (1995), 651–670. MR1312545DOI10.1006/jmaa.1995.1043
- Hudzik H., Pallaschke D., 10.1002/mana.3211860110, Math. Nachr. 186 (1997), 167–185. MR1461219DOI10.1002/mana.3211860110
- Fan K., Glicksberg I., Some geometric properties of the spheres in a normed linear space, Duke Math. J., 25 (1958), 553–568. Zbl0084.33101MR0098976
- Kaminska A., The criteria for local uniform rotundity of Orlicz spaces, Studia Math. 74 (1984), 201–215. Zbl0573.46014MR0781718
- Kaminska A., On some convexity properties of Musielak-Orlicz spaces, Suppl. Rend. Circ. Mat. Palermo (2) 1984, Suppl. No. 5, 63–72. Zbl0573.46015MR0781940
- Megginson R.E., 10.1007/978-1-4612-0603-3, Graduate Texts in Mathematics, 183, Springer, New York, 1998. Zbl0910.46008MR1650235DOI10.1007/978-1-4612-0603-3
- Morsli M., On some convexity properties of the Besicovitch-Orlicz space of almost periodic functions, Comment. Math. Prace Mat. 34 (1994), 137–152. Zbl0839.46012MR1325081
- Morsli M., Bedouhene F., On the strict convexity of the Besicovitch-Orlicz space of almost periodic functions with Orlicz norm, Rev. Mat. Complut. 16 (2003), no. 2, 399–415. Zbl1061.46029MR2032925
- Morsli M., Bedouhene F., 10.4064/cm102-1-9, Colloq. Math. 102 (2005), no. 1, 97–111. Zbl1112.46013MR2150272DOI10.4064/cm102-1-9
- Morsli M., On modular approximation property in the Besicovitch-Orlicz space of almost periodic functions, Comment. Math. Univ. Carolin. 38 (1997), no. 3, 485–496. Zbl0937.46009MR1485070
- Pluciennik R., Wang T.F., Zhang Y.L., H-point and denting points in Orlicz spaces, Comment. Math. Prace Mat. 33 (1993), 135–151. MR1269408
Citations in EuDML Documents
top- Fazia Bedouhene, Amina Daoui, Hocine Kourat, On some convexity properties in the Besicovitch-Musielak-Orlicz space of almost periodic functions with Luxemburg norm
- Slimane Hassaine, Fatiha Boulahia, Extreme points of the Besicovitch--Orlicz space of almost periodic functions equipped with the Luxemburg norm
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.