  Let the Sobolev-type inner product <f,g> = \int fg d mu_0+ int f' g' d mu_1
with mu_0 = w + M delta_c, mu_1= N delta_c 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.
