We consider the homogeneouse space G/H equipped with a strongly quasi-invariant Radon measure µ, where G is a locally compact group and H is a compact subgroup of G. Let 1 ≤ p < ∞ and ω is a weight function on the homogeneous space G/H. Here, we give a sufficient condition for that the weighted Lp-space Lp ω(G/H) is a Banach algebra, i.e. for 1 ≤ p < ∞, we introduce a new Beurling algebras Lp ω(G/H).
