On the multipliers of the Figa-Talamanca Herz algebra

TL;DR

This paper investigates the multiplier properties of the Figa-Talamanca Herz algebra, establishing that for certain p and q, the algebra A_q(G) acts as a multiplier on A_p(G), thus forming a Banach module.

Contribution

It proves that A_q(G) multiplies A_p(G) and that A_p(G) is a Banach module over A_q(G) for specific p and q ranges.

Findings

A_q(G) acts as a multiplier on A_p(G)

A_p(G) forms a Banach module over A_q(G)

The result holds for specified p and q ranges

Abstract

Let $G$ be a locally compact group and $p,q\in \mathbb{R}$ with $p>1$ $p\not=2$ and $q$ between $2$ and $p$ (if $p<2$ then $p<q<2$, if $p>2$ then $2<q<p.$) The main result of the paper is that $A_q(G)$ multiplies $A_p(G)$, more precisely we show that the Banach algebra $A_p(G)$is a Banach module on $A_q(G).$