Abstract : In this paper, we suppose that H is a compact subgroup of locally compact topological group G and GH is a homogeneous space which is equipped with a strongly quasi-invariant Radon measure .Then in the group algebra L1(G), we replace the homogeneouse space GH instead of G and consider the new Banach algebra L1(GH). We study this Banach algebra and its dual. At the end, by characterization of L (GH) and the left and right dual L1(GH)-module actions of L (GH), we give a necessary and su cient conditions for amenability and weak amenability of this Banach algebra.
