In  this paper we define the $p$-analog of the restericted reperesentations and also the $p$-analog of the Fourier--Stieltjes algebras on the inverse semigroups . We improve some results about Herz algebras on Clifford semigroups. At the end of this paper we give the necessary and sufficient condition for amenability of these algebras on Clifford semigroups.

the mixed-signal circuits with both analog and digital blocks on a single chip have wide applications in communication and rf circuits. integrating these two blocks can cause serious problems especially in applications requiring fast digital circuits and high performance analog blocks. fast switching in digital blocks generates a noise which can be introduced to analog circuits by the common su...