# On the functorial properties of the p-analog of the Fourier-Stieltjes algebras and their homomorphisms

## TL;DR

This paper explores the functorial properties of p-analog Fourier-Stieltjes algebras, generalizing existing theories to establish p-complete boundedness of certain maps and homomorphisms induced by piecewise affine maps.

## Contribution

It extends the theory of p-analog Fourier-Stieltjes algebras by generalizing definitions and theorems, and proves p-complete boundedness of homomorphisms from piecewise affine maps.

## Key findings

- Generalized definitions and theorems for p-analog Fourier-Stieltjes algebras.
- Proved p-complete boundedness of certain algebra maps.
- Established p-complete boundedness of homomorphisms from piecewise affine maps.

## Abstract

In this paper, we follow two main goals. In the first attempt, we give some functorial properties of the $p$-analog of the Fourier-Stieltjes algebras in which we generalize some previously existed definitions and theorems in Arsac and Cowling's works, to utilize them to prove $p$-complete boundedness of some well-known maps on these algebras. In the second part, as an application of these generalizations, we prove $p$-completely boundedness of homomorphisms which are induced by continuous and proper piecewise affine maps that is a generalization of Ilie's work on Fig\`a-Talamanca-Herz algebras.