The Canonical Mapping TH for Weighted LP-Spaces the General Case

Let G be a locally compact group and H be a closed subgroup of G. It is well-known that G/H as a homogeneous space admits a strongly quasi invariant measure and the linear mapping TH of L'(G) into L'(G/H) is bounded and surjective. In this note it is shown that by means of complex interpolation theorem, that under restrictions on weight function w, the mapping Th of weighted spaces LP (G,w) into LP(G/H,w) is well-defined, bounded linear and surjective, for 1