  In the context of the Dunkl transform a complete orthogonal system arises in
a very natural way. This paper studies the weighted norm convergence of the
Fourier series expansion associated to this system. We establish conditions on
the weights, in terms of the $A_p$ classes of Muckenhoupt, which ensure the
convergence. Necessary conditions are also proved, which for a wide class of
weights coincide with the sufficient conditions.
