The Uniform Convergence of Fourier Series in a System of the Sobolev Orthogonal Polynomials Associated to Ultraspherical Jacobi Polynomials

We obtain some necessary and sufficient conditions on a parameter  $ \alpha $ that ensure that Fourier series in the Sobolev system of polynomialsassociated to the ultraspherical Jacobi polynomialsconverge uniformly on  $ [-1,1] $ to functions in the Sobolev space $ W^{r}_{L^{1}_{\rho(\alpha)}} $ ,where $ \rho(\alpha) $ is the ultraspherical weight.