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

A. Daoui; Mohamed Morsli; M. Smaali

Commentationes Mathematicae Universitatis Carolinae (2012)

  • Volume: 53, Issue: 2, page 237-251
  • ISSN: 0010-2628

Abstract

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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.

How to cite

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Daoui, A., Morsli, Mohamed, and Smaali, M.. "Duality properties and Riesz representation theorem in Besicovitch-Musielak-Orlicz space of almost periodic functions." Commentationes Mathematicae Universitatis Carolinae 53.2 (2012): 237-251. <http://eudml.org/doc/246380>.

@article{Daoui2012,
abstract = {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.},
author = {Daoui, A., Morsli, Mohamed, Smaali, M.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Orlicz norm; Amemiya norm; conjugate function; Besicovitch-Musielak-Orlicz spaces; almost periodic functions; reflexivity; Riesz theorem; Orlicz norm; Amemiya norm; conjugate function; Besicovitch-Musielak-Orlicz space; almost periodic function; reflexivity; Riesz representation theorem},
language = {eng},
number = {2},
pages = {237-251},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Duality properties and Riesz representation theorem in Besicovitch-Musielak-Orlicz space of almost periodic functions},
url = {http://eudml.org/doc/246380},
volume = {53},
year = {2012},
}

TY - JOUR
AU - Daoui, A.
AU - Morsli, Mohamed
AU - Smaali, M.
TI - Duality properties and Riesz representation theorem in Besicovitch-Musielak-Orlicz space of almost periodic functions
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2012
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 53
IS - 2
SP - 237
EP - 251
AB - 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.
LA - eng
KW - Orlicz norm; Amemiya norm; conjugate function; Besicovitch-Musielak-Orlicz spaces; almost periodic functions; reflexivity; Riesz theorem; Orlicz norm; Amemiya norm; conjugate function; Besicovitch-Musielak-Orlicz space; almost periodic function; reflexivity; Riesz representation theorem
UR - http://eudml.org/doc/246380
ER -

References

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  1. Besicovitch A.S., Almost Periodic Functions, Cambridge Univ. Press, Cambridge, 1932. Zbl0065.07102
  2. Corduneanu C., Gheorghiu N., Barbu V., Almost Periodic Functions, Publishing Company, Chelsea, 1989. Zbl0672.42008MR0481915
  3. Fan X.L., 10.1007/s10114-005-0865-1, Acta Math. Sin. 23 (2007), no. 2, 281–288. Zbl1129.46020MR2286921DOI10.1007/s10114-005-0865-1
  4. Hillmann T.R., Besicovitc-Orlicz spaces of almost periodic functions, Real and Stochastic Analysis, Wiley, New York, 1986, pp. 119–167. MR0856581
  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. Zbl0484.46031MR0646335
  6. Hudzik H., Kaminska A., On uniformly convexifiable and B-convex Musielak-Orlicz spaces, Comment. Math. Prace Mat. 25 (1985), 59–75. Zbl0588.46022MR0795121
  7. Hudzik H., Maligranda L., 10.1016/S0019-3577(00)80026-9, Indag. Math. 11 (2000), no. 4, 573–585. Zbl1010.46031MR1909821DOI10.1016/S0019-3577(00)80026-9
  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. Zbl1090.46010MR1903310
  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. 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
  11. Musielak J., Orlicz Spaces and Modular Spaces, Lecture Notes in Mathematics, 1034, Springer, Berlin, 1983. Zbl0557.46020MR0724434

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