An Lp version of Hardy's theorem for the Dunkl transform

In this paper, we give a generalization of Hardy's theorems for the Dunkl transform F-D on R-d. More precisely for all a > 0, b > 0 and p, q is an element of [ 1, + infinity], we determine the measurable functions f on R-d, such that e(aparallel toxparallel to2) f is an element of L-k(p) (R-d) and e(bparallel toyparallel to2) F-D(f) is an element of L-k(q) (R-d), where L-k(p) (R-d) are the Lebesgue spaces associated with the Dunkl transform.