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# Sur les transformées de Riesz sur les groupes de Lie moyennables et sur certains espaces homogènes

Published:1998-10-01
Printed: Oct 1998
• Noël Lohoué
• Sami Mustapha
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## Abstract

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 - Analysis on real and complex Lie groups [See also 33C80, 43-XX] 35H05 - unknown classification 35H0543A80 - Analysis on other specific Lie groups [See also 22Exx] 43A85 - Analysis on homogeneous spaces