The homogeneous 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 is considered. The weighted L^p-spaces L^p_ω(G/H) for 1 ≤ p < ∞ are introduced and the suitable conditions for these spaces to become Banach algebras are investigated. In this direction a new class of Beurling algebras is introduced and then some fundamental properties of the new class of Beurling algebras are characterized.
