In this paper, we consider Dunkl theory on R^d associated to a finite
reflection group. This theory generalizes classical Fourier anal- ysis. First,
we give for 1 < p <= 2, sufficient conditions for weighted Lp-estimates of the
Dunkl transform of a function f using respectively the modulus of continuity of
f in the radial case and the convolution for f in the general case. In
particular, we obtain as application, the integrability of this transform on
Besov-Lipschitz spaces. Second, we provide necessary and sufficient conditions
on nonnegative functions phi defined on [0; 1] to ensure the boundedness of the
generalized Ces\`aro operator C_phi on Herz spaces and we obtain the
corresponding operator norm inequalities.Comment: 19 page