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 $t_h$ of $l^1(g)$ into $l^1(g/h)$ is bounded and surjective‎. ‎in this note it is shown that by means of complex interpolation theorem‎, ‎that under restrictions on weight function $omega$‎, ‎the mapping $t_h$ of weighted spaces $l^p(g,omega)$ into $l^p(g/h,varpi)$ is well-defined‎, ‎bounded linear and surjective‎ , ‎for $1leq p leq infty$‎.