Journal of the Iranian Mathematical Society

Journal of the Iranian Mathematical Society

Boundedness of composition operators on $X^\Phi$ spaces

Document Type : Research Article

Authors
A. Bagheri salec 1
S. M. Tabatabaie 1
L'aszl'o Szekelyhidi 2
A. H. K. Alhusseini 1
1 Department of Mathematics‎, ‎University of Qom‎, ‎Qom‎, ‎Iran.
2 Debrecen University‎, ‎Department of Mathematics‎, ‎Debrecen‎, ‎Hungary.
10.30504/jims.2024.476597.1205
Abstract
In this paper‎, ‎we study composition operators on the space $X^\Phi$‎, ‎where $\Phi$ is a Young function and $X^\Phi$ is a generalized Orlicz space associated to a Banach function space $X$‎. We give some necessary and sufficient conditions for a composition operator to be bounded on $X^\Phi$‎.
Keywords
Banach function spaces
Composition operator
Generalized Orlicz spaces
Subjects
[1] A. R. Bagheri Salec, C.-C. Chen and S. M. Tabatabaie, Orlicz algebras associated to a Banach function space, Hacet. J. Math. Stat. 53 (2024), no.1, 191–200.
[2] A. R. Bagheri Salec, S. Ivkovi´c and S. M. Tabatabaie, Spaceability on some classes of Banach spaces, Math. Ineq. App. 25 (2022), no. 3, 659–672.
[3] C. Bennettt and R. Sharpley, Interpolation of Operators, Academic Press Inc., New York, 1988.
[4] R. del Campo, A. Fernández, F. Mayoral and F. Naranjo, Orlicz spaces associated to a quasi-Banach function space: Applications to vector measures and interpolation, Collect. Math. 72 (2021), no. 3, 481–499.
[5] T. Chawziuk, Y. Estaremi, H. Hudzik, S. Maghsoudi, I. Rahmani, Basic properties of multiplication and composition operators between distinct Orlicz spaces, Rev. Mat. Complut. 30 (2017), no. 2, 335–367
[6] T. Chawziuk, Y. Cui, Y. Estaremi and H. Hudzik and R. Kaczmarek, Composition and multiplication operators between Orlicz function spaces, J. Inequal. Appl. 52 (2016) 1–18.
[7] J. B. Conway, A Course in Functional Analysis, Springer-Verlag, New York, 1985.
[8] Y. Cui, H. Hudzik, R. Kumar and L. Maligranda, Composition operators in Orlicz spaces, J. Aust. Math. Soc. 76 (2004), no. 2. 189–206.
[9] Y. Cui, H. Hudzik, R. Kumar and R. Kumar, Compactness and essential norms of composition operators on Orlicz-Lorentz spaces, Appl. Math. Lett. 25 (2012), no. 11, 1778–1783.
[10] N. Dunford and J. T. Schwartz, Linear operators, Part I, General Theory Interscience, John Wiley & Sons, Inc., New York, 1958.
[11] S. Gupta, B. S. Komal and N. Suri, Weighted composition operators on Orlicz spaces Int. J. Contemp. Math. Sci. 5 (2010), no. 1-4, 11–20.
[12] P. Jain, L. E. Persson and P. Upreti, Inequalities and properties of some generalized Orlicz classes and spaces, Acta Math. Hungar. 117 (2007), no. 1-2, 161–174.
[13] R. Kumar, Composition operators on Orlicz spaces, Integr. Equ. Oper. Theory 29 (1997), no. 1, 17–22.
[14] R. Kumar and R. Kumar, Composition operators on Orlicz-Lorentz spaces, Integr. Equ. Oper. Theory 60 (2008), 1, 79–88.
[15] R. K. Singh, Composition operators induced by rational functions, Proc. Amer. Math. Soc. 59 (1976), no. 2, 329–333.
[16] S. M. Tabatabaie and A. R. Bagheri Salec, The inclusions of XΦ spaces, Math. Bohem. 148 (2023), no. 1, 65–72.
Journal of the Iranian Mathematical Society
Volume 6, Issue 1
January 2025
Pages 1-7