| Title:
|
Duality properties and Riesz representation theorem in Besicovitch-Musielak-Orlicz space of almost periodic functions (English) |
| Author:
|
Daoui, A. |
| Author:
|
Morsli, M. |
| Author:
|
Smaali, M. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
53 |
| Issue:
|
2 |
| Year:
|
2012 |
| Pages:
|
237-251 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
This paper is an extension of the work done in [Morsli M., Bedouhene F., Boulahia F., Duality properties and Riesz representation theorem in the Besicovitch-Orlicz space of almost periodic functions, Comment. Math. Univ. Carolin. 43 (2002), no. 1, 103--117] to the Besicovitch-Musielak-Orlicz space of almost periodic functions. Necessary and sufficient conditions for the reflexivity of this space are given. A Riesz type ``duality representation theorem'' is also stated. (English) |
| Keyword:
|
Orlicz norm |
| Keyword:
|
Amemiya norm |
| Keyword:
|
conjugate function |
| Keyword:
|
Besicovitch-Musielak-Orlicz spaces |
| Keyword:
|
almost periodic functions |
| Keyword:
|
reflexivity |
| Keyword:
|
Riesz theorem |
| MSC:
|
42A75 |
| MSC:
|
46B20 |
| idZBL:
|
Zbl 1265.46050 |
| idMR:
|
MR3017257 |
| . |
| Date available:
|
2012-08-08T09:00:57Z |
| Last updated:
|
2014-07-07 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/142887 |
| . |
| Reference:
|
[1] Besicovitch A.S.: Almost Periodic Functions.Cambridge Univ. Press, Cambridge, 1932. Zbl 0065.07102 |
| Reference:
|
[2] Corduneanu C., Gheorghiu N., Barbu V.: Almost Periodic Functions.Publishing Company, Chelsea, 1989. Zbl 0672.42008, MR 0481915 |
| Reference:
|
[3] Fan X.L.: Amemiya norm equals Orlicz norm in Musielak-Orlicz spaces.Acta Math. Sin. 23 (2007), no. 2, 281–288. Zbl 1129.46020, MR 2286921, 10.1007/s10114-005-0865-1 |
| Reference:
|
[4] Hillmann T.R.: Besicovitc-Orlicz spaces of almost periodic functions.Real and Stochastic Analysis, Wiley, New York, 1986, pp. 119–167. MR 0856581 |
| Reference:
|
[5] Hudzik H.: Musielak-Orlicz spaces isomorphic to strictly convex spaces.Bull. Acad. Polon. Sci. Sér. Sci. Math. 29 (1981), no. 9–10, 465–470. Zbl 0484.46031, MR 0646335 |
| Reference:
|
[6] Hudzik H., Kaminska A.: On uniformly convexifiable and B-convex Musielak-Orlicz spaces.Comment. Math. Prace Mat. 25 (1985), 59–75. Zbl 0588.46022, MR 0795121 |
| Reference:
|
[7] Hudzik H., Maligranda L.: Amemiya norm equals Orlicz norm in general.Indag. Math. 11 (2000), no. 4, 573–585. Zbl 1010.46031, MR 1909821, 10.1016/S0019-3577(00)80026-9 |
| Reference:
|
[8] Morsli M., Bedouhene F., Boulahia F.: Duality properties and Riesz representation theorem in the Besicovitch-Orlicz space of almost periodic functions.Comment. Math. Univ. Carolin. 43 (2002), no. 1, 103–117. Zbl 1090.46010, MR 1903310 |
| Reference:
|
[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. MR 2287686 |
| Reference:
|
[10] 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. Zbl 1199.46045, MR 2374126 |
| Reference:
|
[11] Musielak J.: Orlicz Spaces and Modular Spaces.Lecture Notes in Mathematics, 1034, Springer, Berlin, 1983. Zbl 0557.46020, MR 0724434 |
| . |
