some relations between l^p-spaces on locally compact group g and double coset k g/h

Let h and k be compact subgroups of locally compact group g. by consideringthe double coset space k g/h , which equipped with an n-strongly quasi invariant measureu, for 1 ⩽ p ⩽ +1, we make a norm decreasing linear map from l^p(g) onto lp(k g;u)and demonstrate that it may be identified with a quotient space of l^p(g). in addition, weillustrate that l^p(k g/h ; u) is isometrically isomorphic to a closed subspace of l^p(g).these assist us to study the structure of the classical banach space created on a double cosetspace by those produced on topological space.