Sur les transformÃ©es de Riesz sur les groupes de Lie moyennables et sur certains espaces homogÃ¨nes Let $\Delta$ be a left invariant sub-Laplacian on a Lie group $G$ and let $\nabla$ be the associated gradient. In this paper we investigate the boundness of the Riesz transform $\nabla\Delta^{-1/2}$ on Lie groups $G$ which are amenable and with exponential volume growth and on certain homogenous spaces. Categories:22E30, 35H05, 43A80, 43A85