Notes on multipliers on weighted Orlicz spaces

Year 2023, Volume: 1 Issue: 1, 20 - 27, 21.06.2023

Büşra Arıs Rüya Üster

https://doi.org/10.26650/ijmath.2023.00002

Abstract

Let 𝐺 be a locally compact abelian group with Haar measure 𝜇, Φ be a Young function and 𝜔 be a weight function. In this paper, we consider the weighted Orlicz space 𝐿 Φ(𝐺, 𝜔) and we investigate the relationship between the multipliers 𝐿1(𝐺, 𝜔)-module and the multipliers on a certain Banach algebra. For this purpose, we firstly define temperate function space with respect to the weighted Orlicz space 𝐿 Φ(𝐺, 𝜔) which we denote by 𝐿 Φ𝑡(𝐺, 𝜔) and give its basic properties. Later, we define a subalgebra of the space of multipliers on 𝐿 Φ(𝐺, 𝜔) and study its basic properties. We also show that this subalgebra is isometrically isomorphic to the space of multipliers of a certain Banach algebra. Moreover, we obtain a characterization for the space of multipliers of 𝐿1(𝐺, 𝜔) ∩ 𝐿 Φ(𝐺, 𝜔).

Keywords

multiplier, weighted Orlicz space, locally compact group

Thanks

We are grateful to anonymous referees for careful reading of the manuscript and for helpful comments.

References

• Başar E., Öztop, S., Uysal, B.H., Yaşar, Ş. 2023, Extreme points in Orlicz spaces equipped with i-norms and its closedness, Mattı. Nachr. 00, 1-21. google scholar
• Dinculeanu, N., 1974, Integration on locally compact spaces, Springer. google scholar
• Feicttinger, H., 1976, Multipliers of Banact spaces of functions on groups, Matt. Z. 152, 47-58. google scholar
• Fisher, M. J., 1974, Properties of three algebras related to Lp-multipliers, Bull. Amer. Math. Soc. 80, 262-265. google scholar
• Griffin, J., McKennon, K., 1973, Multipliers and the group Lp-algebras, Pacific J. Math. 49, 365-370. google scholar
• Larsen, R., 1971, An introduction to the theory of multipliers, Die Grundlehren der mathematischen Wissenschaften, 175, Springer-Verlag, Berlin, Heidelberg and New York. google scholar
• McKennon, K., 1972, Multipliers of type (p,p)0, Pacific J. Math. 43, 429-436. google scholar
• Osançlıol, A., Öztop, S., 2015, Weighted Orlicz algebras on locally compact groups, Journal of Australian Mathematical Society, 99, 399-414. google scholar
• Öztop, S., 2003, A note on multipliers of Lp (G, A), J. Aust. Math. Soc., 74, 25-34. google scholar
• Öztop, S., Samei, E., 2017, Twisted Orlicz algebras I, Studia Mathematica, 236, 271-296. google scholar
• Öztop, S., Samei, E., 2019, Twisted Orlicz algebras II, Mathematische Nachrichten, 292, 1122-1136. google scholar
• Rao, M. M., Ren, Z. D., 1991, Theory of Orlicz spaces, Marcel Dekker, New York. google scholar
• Reiter H., Stegeman J. D., 2000, Classical harmonic analysis and locally compact groups, Clarendon Press, Oxford. google scholar
• Üster, R., Öztop, S., 2020, Invariant subsets and homological properties of Orlicz modules over group algebras, Taiwanese Journal of Mathematics, 24, 959-973. google scholar
• Üster, R., 2021, Multipliers for the weighted Orlicz spaces of a locally compact abelian group, Results in Mathematics, 76 (4), Paper No. 183. google scholar
• Wang, J. K., 1961, Multipliers of commutative Banach algebras, Pacific J. Math. 11, 1131-114. google scholar