Abstract. Let H be a compact subgroup of a locally compact group G. We consider the homogeneous space G/H equipped with a strongly quasi-invariant Radon measure µ. For 1 ≤ p ≤ +∞, we introduce a norm decreasing linear map from Lp(G) onto Lp(G/H,µ) and show that Lp(G/H,µ) may be identified with a quotient space of Lp(G). Also, we prove that Lp(G/H,µ) is isometrically isomorphic to a closed subspace of Lp(G). These help us study the structure of the classical Banach spaces constructed on a homogeneous space via those created on topological groups.
