Generalization of Titchmarsh’s theorem for the Jacobi transform in the space Lp (α,β)(R+)

Abstract

Using a generalized translation operator, we obtain a generalization of Titchmarsh’s theorem for the Jacobi transform in the space Lp(R+,Δ(α,β)(t)dt) for functions satisfying the (γ, p)-Jacobi Lipschitz condition.