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Search: MSC category 43A80 ( Analysis on other specific Lie groups [See also 22Exx] )

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1. CJM 2000 (vol 52 pp. 412)

Varopoulos, N. Th.
Geometric and Potential Theoretic Results on Lie Groups
The main new results in this paper are contained in the geometric Theorems 1 and~2 of Section~0.1 below and they are related to previous results of M.~Gromov and of myself (\cf\ \cite{1},~\cite{2}). These results are used to prove some general potential theoretic estimates on Lie groups (\cf\ Section~0.3) that are related to my previous work in the area (\cf\ \cite{3},~\cite{4}) and to some deep recent work of G.~Alexopoulos (\cf\ \cite{5},~\cite{21}).

Categories:22E30, 43A80, 60J60, 60J65

2. CJM 1998 (vol 50 pp. 1090)

Lohoué, Noël; Mustapha, Sami
Sur les transformées de Riesz sur les groupes de Lie moyennables et sur certains espaces homogènes
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

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