Let G be a metrizable locally compact Abelian group with dual group G. [...] denotes the vector space of all complex-valued functions in L1 (G) whose Fourier transforms [...] belong to LP(G). Research on the spaces Ap(G) was initiated by Warner in  and Larsen, Liu and Wang in , Martin and Yap in . Let Lip(alpha,p) and lip(alpha,p) denote the Lipschitz spaces defined on G. In the present paper, the space Alip/p(G) consisting of all complex-valued functions [...] whose Fourier transforms [...] belong to Lp(G) is investigated. In the first section invariant properties and asymptotic estimates for the translation and modulation operators are given. Furthermore it is showed that space App(G) is homogeneous Banach space. At the end of this work, it is proved that the space of all multipliers from L1 (G) to Alip/p(G) is the space Alip/p(G).