Orlicz algebras associated to a Banach function space

Year 2024, Volume: 53 Issue: 1, 191 - 200, 29.02.2024

Chung-chuan Chen , Alireza Bagheri Salec , Seyed Mohammad Tabatabaie

https://doi.org/10.15672/hujms.1018098

Abstract

In this paper, we study the spaces ${\mathcal X}^\Phi$ as Banach algebras, where $\mathcal X$ is a quasi-Banach function space and $\Phi$ is a Young function, and extend some well-known facts regarding Lebesgue and Orlicz spaces on this new structure. Also, for each $p\geq 1$, we give some necessary condition for the space $\mathcal{X}^p$ to be a Banach algebra under the pointwise product.

Keywords

convolution algebra, Orlicz space, Young function, PCS-space, Banach algebra, locally compact group, spaceability, pointwise product

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