Duality properties and Riesz representation theorem in the Besicovitch-Orlicz space of almost periodic functions

Mohamed Morsli; Fazia Bedouhene; Fatiha Boulahia

Commentationes Mathematicae Universitatis Carolinae (2002)

  • Volume: 43, Issue: 1, page 103-117
  • ISSN: 0010-2628

Abstract

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In [6], the classical Riesz representation theorem is extended to the class of Besicovitch space of almost periodic functions B q  a.p., q ∈ ] 1 , + ∞ [ . It is also shown that this space is reflexive. We shall consider here such results in the context of Orlicz spaces, namely in the class of Besicovitch-Orlicz space of almost periodic functions B φ  a.p., where φ is an Orlicz function.

How to cite

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Morsli, Mohamed, Bedouhene, Fazia, and Boulahia, Fatiha. "Duality properties and Riesz representation theorem in the Besicovitch-Orlicz space of almost periodic functions." Commentationes Mathematicae Universitatis Carolinae 43.1 (2002): 103-117. <http://eudml.org/doc/249002>.

@article{Morsli2002,
abstract = {In [6], the classical Riesz representation theorem is extended to the class of Besicovitch space of almost periodic functions $B^\{q\}$ a.p., $q\in ] 1,+\infty [$ . It is also shown that this space is reflexive. We shall consider here such results in the context of Orlicz spaces, namely in the class of Besicovitch-Orlicz space of almost periodic functions $B^\{\phi \}$ a.p., where $\phi $ is an Orlicz function.},
author = {Morsli, Mohamed, Bedouhene, Fazia, Boulahia, Fatiha},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Besicovitch-Orlicz space; almost periodic function; reflexivity; duality; dual Besicovitch-Orlicz space; reflexive Besicovitch-Orlicz space},
language = {eng},
number = {1},
pages = {103-117},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Duality properties and Riesz representation theorem in the Besicovitch-Orlicz space of almost periodic functions},
url = {http://eudml.org/doc/249002},
volume = {43},
year = {2002},
}

TY - JOUR
AU - Morsli, Mohamed
AU - Bedouhene, Fazia
AU - Boulahia, Fatiha
TI - Duality properties and Riesz representation theorem in the Besicovitch-Orlicz space of almost periodic functions
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2002
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 43
IS - 1
SP - 103
EP - 117
AB - In [6], the classical Riesz representation theorem is extended to the class of Besicovitch space of almost periodic functions $B^{q}$ a.p., $q\in ] 1,+\infty [$ . It is also shown that this space is reflexive. We shall consider here such results in the context of Orlicz spaces, namely in the class of Besicovitch-Orlicz space of almost periodic functions $B^{\phi }$ a.p., where $\phi $ is an Orlicz function.
LA - eng
KW - Besicovitch-Orlicz space; almost periodic function; reflexivity; duality; dual Besicovitch-Orlicz space; reflexive Besicovitch-Orlicz space
UR - http://eudml.org/doc/249002
ER -

References

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  1. Albrycht J., The theory of Marcinkiewicz Orlicz spaces, Dissertationes Math., No. 27 (1962). Zbl0101.32803MR0139935
  2. Besicovitch A.S., Almost Periodic Functions, Dover Pub. Inc., NewYork, 1954. Zbl0065.07102MR0068029
  3. Chen S., Geometry of Orlicz spaces, Dissertationes Math., No. 356 (1996). Zbl1089.46500MR1410390
  4. Hillmann T.R., Besicovitch-Orlicz spaces of almost periodic functions, Real and Stochastic Analysis, Wiley, 1986, pp. 119-167. Zbl0656.46020MR0856581
  5. Hudzik H., Kaminska A., On uniformly convexifiable and B -convex Musielak-Orlicz spaces, Comment. Math. 25 (1985), 59-75. (1985) Zbl0588.46022MR0795121
  6. Iannacci R., About reflexivity of B q a . p . spaces of almost periodic function, Rend. Mat. Appl. (7) 13 3 543-559 (1993). (1993) MR1276259
  7. Krasnosel'skii M.A., Rutickii Ya.B., Convex function and Orlicz spaces (translation), P. Noodhoff Ltd., Groningen, 1961. MR0126722
  8. Morsli M., On some convexity properties of the Besicovitch-Orlicz space of almost periodic functions, Comment. Math. 34 (1994), 137-152. (1994) Zbl0839.46012MR1325081
  9. Morsli M., Espace de Bésicovitch Orlicz de fonctions presque périodiques. Structure générale et géométrie, Thèse de Doctorat, 1996. 
  10. Morsli M., On modular approximation property in the Besicovitch-Orlicz space of almost periodic functions, Comment. Math. Univ. Carolinae 38.3 (1997), 485-496. (1997) Zbl0937.46009MR1485070
  11. Musielak J., Orlicz W., On modular spaces, Studia Math. 18 49-65 (1959). (1959) Zbl0099.09202MR0101487
  12. Rao M.M., Ren Z.D., Theory of Orlicz Spaces, Marcel Dekker, Inc., New-York, 1991. Zbl0724.46032MR1113700

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