Orlicz algebras associated to a Banach function space

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

References

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