A Cohen type inequality for Laguerre–Sobolev expansions

Let introduce the Sobolev type inner product〈f,g〉=∫0∞f(x)g(x)dμ(x)+Mf(0)g(0)+Nf′(0)g′(0), wheredμ(x)=1Γ(α+1)xαe−xdx,M,N⩾0,α>−1. In this paper we prove a Cohen type inequality for the Fourier expansion in terms of the orthonormal polynomials associated with the above Sobolev inner product. In particular, for M=N=0M=N=0, we extend the result of Markett [C. Markett, Cohen type inequalities for Jacobi, Laguerre and Hermite expansions, SIAM J. Math. Anal. 14 (1983) 819–833].