Abstract
Let the Sobolev-type inner product " where w is the Jacobi weight, c is either 1 or -1 and M, N ≥ 0. We obtain estimates and asymptotic properties on [-1, 1] for the polynomials orthonormal with respect to (.,.) and their kernels. We also compare these polynomials with Jacobi orthonormal polynomials; as a consequence, a result about the convergence acceleration to c of the zeros is given.