BSE property for some certain Segal algebras with applications to the Fourier algebra

TL;DR

This paper investigates the BSE-property in specific Segal algebras, explores its implications for subalgebras of the Fourier algebra, and extends existing results to a broader class of Banach algebras.

Contribution

It introduces new conditions for the BSE-property in Segal algebras and generalizes previous results related to Fourier algebra subalgebras.

Findings

Identified new classes of Banach algebras with the BSE-property

Extended Kaniuth and Ulger's results to more general settings

Provided applications to Fourier algebra subalgebras

Abstract

In this paper, we study the BSE-property for some certain Segal algebras. As an application, we give some results on subalgebras of the Fourier algebra and provide a wide range of Banach algebras with the BSE-property. Also, we give a generalization of a result due to E. Kaniuth and A. \"Ulger.