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

Abstract

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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.

How to cite

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Bedouhene, 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

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  10. Kaminska A., On some convexity properties of Musielak-Orlicz spaces, Suppl. Rend. Circ. Mat. Palermo (2) 1984, Suppl. No. 5, 63–72. Zbl0573.46015MR0781940
  11. 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
  12. 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
  13. 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
  14. Morsli M., Bedouhene F., 10.4064/cm102-1-9, Colloq. Math. 102 (2005), no. 1, 97–111. Zbl1112.46013MR2150272DOI10.4064/cm102-1-9
  15. 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
  16. 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

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