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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  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
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