A Cohen type inequality for Laguerre–Sobolev expansions

Let introduce the Sobolev type inner product 〈 f , g 〉 = ∫ 0 ∞ f ( x ) g ( x ) d μ ( x ) + M f ( 0 ) g ( 0 ) + N f ′ ( 0 ) g ′ ( 0 ) , where d μ ( x ) = 1 Γ ( α + 1 ) x α e − x d x , 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 = 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].