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In this paper we investigate the compact and weakly compact multipliers ofthe Herz-algebras $A_p(G)$. Let $B_p(G)$ be the space of pointwise multipliersof $A_p(G)$. We show that there is a topological invariant mean on $B^*_p (G)$.Furthermore, we show that if $B^*_p(G)$ is separable, then $G$ is a discretegroup.

Topological Invariant Means on dual Space of Multiplier algebra and weakly compact Multiplier on Herz-algebra