A Cohen type inequality for Laguerre-Sobolev expansions with a mass point outside their oscillatory regime

Let consider the Sobolev type inner product \langle f, g\rangle_S = \int_0^{\infty} f(x)g(x)d \mu (x) + Mf(c)g(c) + Nf^{\prime}(c) g^{\prime}(c), where d\mu (x) = x^{\alpha} e^{-x}dx, \alpha > -1, is the Laguerre measure, c < 0, and M, N \geq 0. In this paper we get a Cohen-type 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 \delta in terms of this kind of Laguerre--Sobolev polynomials.Supported by Fundaçao para a Ciencia e a Tecnologia (FCT) of Portugal, ref. SFRH/BPD/91841/2012, and partially supported by Dirección General de Investigación Científica, Ministerio de Economía y Competitividad of Spain, grant MTM 2012-36732-C03-01. Supported by the Research Fellowship Program, Ministerio de Ciencia e Innovación (MTM 2009-12740-C03-01