  We study multiplier algebras for a large class of Banach algebras which
contains the group algebra $L_1(G)$, the Beurling algebras $L_1(G, \omega)$,
and the Fourier algebra $A(G)$ of a locally compact group $G$. This study
yields numerous new results and unifies some existing theorems on $L_1(G)$ and
$A(G)$ through an abstract Banach algebraic approach. Applications are obtained
on representations of multipliers over locally compact quantum groups and on
topological centre problems. In particular, five open problems in abstract
harmonic analysis are solved.
