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.

MSC Classifications:

22E30, 35H05, 43A80, 43A85 show english descriptions Analysis on real and complex Lie groups [See also 33C80, 43-XX]
unknown classification 35H05
Analysis on other specific Lie groups [See also 22Exx]
Analysis on homogeneous spaces 22E30 - Analysis on real and complex Lie groups [See also 33C80, 43-XX]
35H05 - unknown classification 35H05
43A80 - Analysis on other specific Lie groups [See also 22Exx]
43A85 - Analysis on homogeneous spaces

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