On the Riesz transforms on the homogeneous spaces of semisimple Lie groups

ON THE RIESZ TRANSFORMS ON THE HOMOGENEOUS SPACES OF SEMISIMPLE LIE GROUPS. - Let G be a semisimple noncompact Lie group with finite center and let H subset of G be a closed subgroup with the same properties. Let Delta = - Sigmax(j)(2) be a left invariant sub-Laplacian on G. In this paper we investigate the boundness of the Riesz transforms associated to the sub-Laplacian Delta on the homogenous space H\G.