Orlicz algebras associated to a Banach function space

Authors : Chungchuan Chen, Alireza Bagheri Salec, Seyed Mohammad Tabatabaie

Pages : 191-200

Doi:10.15672/hujms.1018098

View : 167 | Download : 304

Publication Date : 2024-02-29

Article Type : Research Paper

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