SEGAL ALGEBRA $\[{A_{1,p}}(G)\]$ AND ITS MULTIPLIERS

Let G be a locally compactb abelian group and $\{A_p}(G)\]$ the p-Fourier algeba of Herz. This pepar studies the space $\{A_{1,p}}(G) = {L_1}(G) \cap {A_p}(G)\]$ with convolution product. It is proved that $\{A_{1,p}}(G)\]$ is a character Segal algebra. Moreover, for the multipliers of $\{A_{1,p}}(G)\]$ the author proves that $\M({A_{1,p}}(G),{L_1}(G)) = M(G)\]$ and $\M({A_{1,p}}(G),{A_{1,p}}(G)) = M(G)\]$ provided G is noncompact. If G is discrete, then $\M({A_{1,p}}(G),{L_1}(G)) = {A_{1,p}}(G)\$ and $\M({A_{1,p}}(G),{A_{1,p}}(G)) = {A_{1,p}}(G)\]$