  In this paper we study $p$-completely boundedness of weighted maps on the
$p$-analog of the Fourier-Stieltjes algebras, based on the $p$-operator
structure defined by the authors. We study $p$-completely boundedness of
homomorphisms, which are induced by continuous and proper piecewise affine
maps, that is a generalization of Ilie's results on Fig\`a-Talamanca-Herz
algebras.
