On the functorial properties of the $p$-analog of the Fourier-Stieltjes algebras

TL;DR

This paper generalizes known results about Fourier-Stieltjes algebras to their $p$-analogues, exploring their functorial properties and dual space connections using ultrafilter theory.

Contribution

It introduces the $p$-analog of the $ au$-Fourier space and establishes key functorial properties of the $p$-Fourier-Stieltjes algebra, extending classical results.

Findings

Generalized the idempotent theorem to $p$-analogues.

Connected dual spaces of $p$-pseudofunctions with $p$-Fourier spaces.

Established significant functorial properties of $p$-Fourier-Stieltjes algebras.

Abstract

In this paper, some known results will be generalized. Firstly, the idempotent theorem on the Fourier-Stieltjes algebra will be promoted and linked to the $p$-analog of such an algebra. Next, the $p$-analog of the $\pi$-Fourier space introduced by Arsac will be given, and by taking advantage of the theory of ultra filters, the connection between the dual space of the algebra of $p$-pseudofunctions and the $p$-analog of the $\pi$-Fourier space, will be fully investigated. As the main result, one of the significant and applicable functorial properties of the $p$-analog of the Fourier-Stieltjes algebras will be achieved.