Orlicz Amalgam Spaces on the Affine Group

Year 2024, Early Access, 1 - 13

Büşra Arıs

https://doi.org/10.15672/hujms.1460222

Abstract

Let A be the affine group, Φ1, Φ2 be Young functions. We study the Orlicz amalgam spaces W (LΦ1 (A), LΦ2 (A)) defined on A, where the local and global component spaces are the Orlicz spaces LΦ1 (A) and LΦ2 (A), respectively. We obtain an equivalent discrete norm on the amalgam space W (LΦ1 (A), LΦ2 (A)) using the constructions related to the affine group. Using the discrete norm we compute the dual space of W (LΦ1 (A), LΦ2 (A)). We also prove that the Orlicz amalgam space is a left L1(A)-module with respect to convolution under certain conditions. Finally, we investigate some inclusion relations between the Orlicz amalgam spaces.

Keywords

Amalgam spaces, Orlicz spaces, affine group, discrete norms, convolution

Thanks

I would like to thank Prof. S. Öztop for critical reading of the manuscript and helpful suggestions on the subject.

References

• [1] B. Ars and S. Öztop, Wiener amalgam spaces with respect to Orlicz spaces on the affine group, J. Pseudo. Differ. Oper. Appl. 14, 23, 2023