  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
$A_q(G).$
