Some Results for the Jacobi-Dunkl Transform in the Space Lp(R, Aα,β (x)dx)

Abstract. In this paper, using a generalized Jacobi-Dunkl translation operator, we obtain a generalization of Titchmarsh’s theorem for the Dunkl transform for functions satisfying the (ϕ, p)-Lipschitz Jacobi-Dunkl condition in the space Lp(R, Aα,β (x)dx), α ≥ β ≥ −1 /2, α≠ −1/2