  In this paper we study several inequalities of log-Sobolev type for Dunkl
operators. After proving an equivalent of the classical inequality for the
usual Dunkl measure $\mu_k$, we also study a number of inequalities for
probability measures of Boltzmann type of the form $e^{-|x|^p} d\mu_k$. These
are obtained using the method of $U$-bounds. Poincar\'e inequalities are
obtained as consequences of the log-Sobolev inequality. The connection between
Poincar\'e and log-Sobolev inequalities is further examined, obtaining in
particular tight log-Sobolev inequalities. Finally, we study application to
exponential integrability and to functional inequalities for a class of
singular Boltzmann-Gibbs measures.
