| Title:
|
Duality properties and Riesz representation theorem in the Besicovitch-Orlicz space of almost periodic functions (English) |
| Author:
|
Morsli, M. |
| Author:
|
Bedouhene, F. |
| Author:
|
Boulahia, F. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
43 |
| Issue:
|
1 |
| Year:
|
2002 |
| Pages:
|
103-117 |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
Besicovitch-Orlicz space |
| Keyword:
|
almost periodic function |
| Keyword:
|
reflexivity |
| Keyword:
|
duality |
| MSC:
|
42A75 |
| MSC:
|
46B20 |
| MSC:
|
46E30 |
| idZBL:
|
Zbl 1090.46010 |
| idMR:
|
MR1903310 |
| . |
| Date available:
|
2009-01-08T19:19:52Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119303 |
| . |
| Reference:
|
[1] Albrycht J.: The theory of Marcinkiewicz Orlicz spaces.Dissertationes Math., No. 27 (1962). Zbl 0101.32803, MR 0139935 |
| Reference:
|
[2] Besicovitch A.S.: Almost Periodic Functions.Dover Pub. Inc., NewYork, 1954. Zbl 0065.07102, MR 0068029 |
| Reference:
|
[3] Chen S.: Geometry of Orlicz spaces.Dissertationes Math., No. 356 (1996). Zbl 1089.46500, MR 1410390 |
| Reference:
|
[4] Hillmann T.R.: Besicovitch-Orlicz spaces of almost periodic functions.Real and Stochastic Analysis, Wiley, 1986, pp. 119-167. Zbl 0656.46020, MR 0856581 |
| Reference:
|
[5] Hudzik H., Kaminska A.: On uniformly convexifiable and $B$-convex Musielak-Orlicz spaces.Comment. Math. 25 (1985), 59-75. Zbl 0588.46022, MR 0795121 |
| Reference:
|
[6] Iannacci R.: About reflexivity of $B^qa.p.$ spaces of almost periodic function.Rend. Mat. Appl. (7) 13 3 543-559 (1993). MR 1276259 |
| Reference:
|
[7] Krasnosel'skii M.A., Rutickii Ya.B.: Convex function and Orlicz spaces (translation).P. Noodhoff Ltd., Groningen, 1961. MR 0126722 |
| Reference:
|
[8] Morsli M.: On some convexity properties of the Besicovitch-Orlicz space of almost periodic functions.Comment. Math. 34 (1994), 137-152. Zbl 0839.46012, MR 1325081 |
| Reference:
|
[9] Morsli M.: Espace de Bésicovitch Orlicz de fonctions presque périodiques. Structure générale et géométrie.Thèse de Doctorat, 1996. |
| Reference:
|
[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. Zbl 0937.46009, MR 1485070 |
| Reference:
|
[11] Musielak J., Orlicz W.: On modular spaces.Studia Math. 18 49-65 (1959). Zbl 0099.09202, MR 0101487 |
| Reference:
|
[12] Rao M.M., Ren Z.D.: Theory of Orlicz Spaces.Marcel Dekker, Inc., New-York, 1991. Zbl 0724.46032, MR 1113700 |
| . |
