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 polynomials associated to the ultraspherical Jacobi polynomials converge uniformly on $[-1,1]$ to functions in the Sobolev space $W^r_{L^1_{\rho(\alpha)}}$, where $\rho(\alpha)$ is the ultraspherical weight.