Generalization of Titchmarsh's Theorem for the Dunkl Transform

Using a generalized spherical mean operator, we obtain a generalization of Titchmarsh's theorem for the Dunkl transform for functions satisfying the ('; p)-Dunkl Lipschitz condition in the space Lp(Rd;wl(x)dx), ۱ < p ۶ ۲, where wl is a weight function invariant under the action of an associated re ection group.

Keywords:

Dunkl transform , generalized spherical mean operator , Dunkl kernel