Some notes about Orlicz spaces related to a Banach function space

Document Type : Original Article

Author

Department of Mathematics, University of Qom, Qom, Iran

Abstract

 Orlicz spaces, as a very important generalization of Lebesgue spaces, were proposed more than 100 years ago and were first introduced by Z. W. Birnbaum and W. Orlicz. َAfter that, another generalization of Lebesgue spaces with symbols X^p instead of L^p was introduced in which X is a Banach function space. In this article, another generalization of Lebesgue spaces is investigated, which includes both previous generalizations. Although this generalization and preliminary studies of it were published in a scientific report in 1988, effective research on this generalization was done 15 years ago. Due to the fact that in this generalization a convex and Young function Φ is placed instead of function |.|^p and a Banach function space X is placed instead of space L^1, in this article, taking into account the conditions of the function Φ we will check properties of generalized Orlicz space X^Φ.

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References

[1] Bagheri Salec, A., Ivkovi´c, S., & Tabatabaie, S.M. (2022). Spaceability on some classes of Banach spaces. Mathematical Inequalities and Applications, 25(3), 659–672. DOI: https://doi.org/10.7153/mia-2022-25-41.
[2] Campo, R.del., Fernández, A., Mayoral, F., & Naranjo, F. (2020). Orlicz spaces associated to a quasi-Banach function space. Applications to vector measures and interpolation. Collect. Math. DOI: https://doi.org/10.1007/s13348-020-00295-1.
[3] Jain, P., Persson, L.E., & Upreti, P. (2007). Inequalities and properties of some generalized Orlicz classes and spaces. Acta Math. Hungar, 117, 161–174. DOI: https://doi.org/10.1007/s10474-007-6083-9.
[4] Rao, M.M., & Ren, Z.D. (1991). Theory of Orlicz Spaces. Marcel Dekker, New York.
[5] Tabatabaie, S.M., & Bagheri Salec, A.R. (2023). On The Inclusions Of XΦ Spaces. Mathematica Bohemica, 148, 65–72. DOI: https://doi.org/https://doi.org/10.21136/MB.2022.0064-21. 
Measure Algebras and Applications
Volume 1, Issue 1 - Serial Number 1
September 2023
Pages 74-82

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History

  • Receive Date: 10 May 2023
  • Revise Date: 01 August 2023
  • Accept Date: 02 August 2023

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