Let consider the Sobolev type inner productwhere dµ(x) = x α e −x dx, α > −1, is the Laguerre measure, c < 0, and M, N ≥ 0 . In this paper we get a Cohentype inequality for Fourier expansions in terms of the orthonormal polynomials associated with the above Sobolev inner product. Then, as an immediate consequence, we deduce the divergence of Fourier expansions and Cesàro means of order δ in terms of this kind of Laguerre-Sobolev polynomials.