Let G be a locally compact Abelian group (nondiscrete and non cotnpact) with dual group G- For 1 < P < ~, A (G) denotes the vector space of ali complex-valued functions in L'(G) whose Fourier transforms f belong to LP(G ). Research on the spaces A (G) was initiated by Warner [20] and Larsen, Liu and Wang [14], Later several generalizations of these spaces to tire weighted case was given by Gürkanlı