Generalized de la Vallée Poussin operators for Jacobi weights

Starting from a natural generalization of the trigonometric case, we construct a de la Vall\'ee Poussin approximation process in the uniform and L1 norms. With respect to the classical approach we obtain the convergence for a wider class of Jacobi weights. Even if we only consider the Jacobi case, our construction is very general and can be extended to other classes of weights.