On some convexity properties in the Besicovitch-Musielak-Orlicz space of almost periodic functions with Luxemburg norm

Fazia Bedouhene; Amina Daoui; Hocine Kourat

Commentationes Mathematicae Universitatis Carolinae (2012)

  • Volume: 53, Issue: 4, page 535-547
  • ISSN: 0010-2628

Abstract

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In this article, it is shown that geometrical properties such as local uniform convexity, mid point local uniform convexity, H-property and uniform convexity in every direction are equivalent in the Besicovitch-Musielak-Orlicz space of almost periodic functions ( B ˜ ϕ a . p . ) endowed with the Luxemburg norm.

How to cite

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Bedouhene, Fazia, Daoui, Amina, and Kourat, Hocine. "On some convexity properties in the Besicovitch-Musielak-Orlicz space of almost periodic functions with Luxemburg norm." Commentationes Mathematicae Universitatis Carolinae 53.4 (2012): 535-547. <http://eudml.org/doc/252526>.

@article{Bedouhene2012,
abstract = {In this article, it is shown that geometrical properties such as local uniform convexity, mid point local uniform convexity, H-property and uniform convexity in every direction are equivalent in the Besicovitch-Musielak-Orlicz space of almost periodic functions $(\widetilde\{B\}^\{\varphi \}a.p.)$ endowed with the Luxemburg norm.},
author = {Bedouhene, Fazia, Daoui, Amina, Kourat, Hocine},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {local uniform convexity; uniform convexity in every direction; mid point locally uniform; H-property; strict convexity; approximation; Besicovitch-Musielak-Orlicz space; almost periodic function; local uniform convexity; midpoint locally uniform convexity; H-property; Besicovitch-Musielak-Orlicz space; almost periodic function},
language = {eng},
number = {4},
pages = {535-547},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On some convexity properties in the Besicovitch-Musielak-Orlicz space of almost periodic functions with Luxemburg norm},
url = {http://eudml.org/doc/252526},
volume = {53},
year = {2012},
}

TY - JOUR
AU - Bedouhene, Fazia
AU - Daoui, Amina
AU - Kourat, Hocine
TI - On some convexity properties in the Besicovitch-Musielak-Orlicz space of almost periodic functions with Luxemburg norm
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2012
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 53
IS - 4
SP - 535
EP - 547
AB - In this article, it is shown that geometrical properties such as local uniform convexity, mid point local uniform convexity, H-property and uniform convexity in every direction are equivalent in the Besicovitch-Musielak-Orlicz space of almost periodic functions $(\widetilde{B}^{\varphi }a.p.)$ endowed with the Luxemburg norm.
LA - eng
KW - local uniform convexity; uniform convexity in every direction; mid point locally uniform; H-property; strict convexity; approximation; Besicovitch-Musielak-Orlicz space; almost periodic function; local uniform convexity; midpoint locally uniform convexity; H-property; Besicovitch-Musielak-Orlicz space; almost periodic function
UR - http://eudml.org/doc/252526
ER -

References

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  1. Bedouhene F., Morsli M., Smaali M., On some equivalent geometric properties in the Besicovitch-Orlicz space of almost periodic functions with Luxemburg norm, Comment. Math. Univ. Carolin. 51 (2010), no. 1, 25–35. Zbl1224.46018MR2666078
  2. Chen S., Geometry of Orlicz spaces, Dissertationes Math. 356 (1996). Zbl1089.46500MR1410390
  3. Daoui A., Morsli M., Smaali M., Duality properties and Riesz representation theorem in the Besicovitch-Musielak-Orlicz space of almost periodic functions, to appear. 
  4. Day M.M., James R.C., Swaminathan S., 10.4153/CJM-1971-109-5, Canad. J. Math. 23 (1971), 1051–1059. Zbl0229.46020MR0287285DOI10.4153/CJM-1971-109-5
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  6. Hillmann T.R., Besicovitch-Orlicz Spaces of Almost Periodic Functions, Real and Stochastic Analysis, Wiley, New York, 1986, pp. 119–167. Zbl0656.46020MR0856581
  7. Kaminska, A., On some convexity properties of Musielak-Orlicz spaces, Rend. Circ. Mat. Palermo (2) (1984), suppl. no. 5, 63–72. Zbl0573.46015MR0781940
  8. Morsli M., Smaali M., Characterization of the strict convexity of the Besicovitch Musielak-Orlicz space of almost periodic functions, Comment. Math. Univ. Carolin. 48 (2007), no. 3, 443–458. Zbl1199.46045MR2374126
  9. Morsli M., Smaali M., Characterization of the uniform convexity of the Besicovitch-Musielak-Orlicz space of almost periodic functions, Comment. Math. Prace Mat.46 (2006), no. 2, 215–231. MR2287686
  10. 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
  11. Cui,Y.T. and Z. Tao, Kadec-Klee property in Musielak-Orlicz spaces equipped with the Luxemburg norm, . Sci. Math. 1,3 (1998) 339-345. MR1688249
  12. Musielak J., Orlicz Spaces and Modular Spaces, Springer, Berlin-Heidelberg-New York-Tokyo, 1983. Zbl0557.46020MR0724434
  13. Musielak J., Orlicz W., On modular spaces, Studia Math. 18 (2003), no. 2, 49–65. Zbl0111.30501MR0101487
  14. Wang T., Teng Y., 10.1007/BF02876036, Science in China 43 (2000), no. 2, 113–121. Zbl1048.46031MR1763089DOI10.1007/BF02876036
  15. Zizler V., On some rotundity and smoothnes properties of Banach spaces, Dissertationes Math. (Rozprawy Mat.) 87 (1971), 5–33. MR0300060

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