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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].