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

Abstract

Let consider the Sobolev type inner product ⟨f, g⟩S = ∫ ∞ 0 f(x)g(x)dµ(x) + Mf(c)g(c) + Nf′ (c)g ′ (c), where 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 Ces`aro means of order δ in terms of this kind of Laguerre Sobolev polynomials