  In this paper we study various forms of the Hardy inequality for Dunkl
operators, including the classical inequality, $L^p$ inequalities, an improved
Hardy inequality, as well as the Rellich inequality and a special case of the
Caffarelli-Kohn-Nirenberg inequality. As a consequence, one-dimensional
many-particle Hardy inequalities for generalised root systems are proved, which
in the particular case of root systems $A_{N-1}$ improve some well-known
results.
