Generalization of Titchmarsh's Theorem for the Dunkl Transform in the Space Lp(Rd;wl(x)dx) [ Generalization of Titchmarsh's Theorem for the Dunkl Transform]

Abstract. Using a generalized spherical mean operator, we obtain a generalization of Titch- marsh's theorem for the Dunkl transform for functions satisfying the (φ; p)-Dunkl Lipschitz condition in the space Lp(Rd;wl(x)dx), 1 < p ⩽ 2, where wl is a weight function invariant under the action of an associated re ection group.