In this paper, some relations between Lp-spaces on locally compact groups are found. Applying these results proves that for a locally compact group G, the convolution Banach algebras Lp(G) ∩ L1(G) (1 < p ≤ ∞), and Ap(G) ∩ L1(G) (1 < p < ∞) are amenable if and only if G is discrete and amenable.
