Multipliers of grand and small Lebesgue spaces

Let $G$ a locally compact abelian group with Haar measure $\mu$ and let $1<p<\mathrm{\infty }\mathrm{.}$ In the present paper we determine necessary and sufficient conditions on $G$ for the grand Lebesgue space $L^{p),\theta }(G)$ to be a Banach algebra under convolution.Later we characterize the multipliers of the grand Lebesgues, $L^{p,)\theta }(G)$ and the small Lebesgue spaces $L^{(P^{\mathrm{\prime }}\theta }$, where $\frac{1}{p}+\frac{1}{p^{\mathrm{\prime }}}=1$