A Cohen Type Inequality for Orthogonal Expansions with Respect to the Generalized Jacobi Weight

Abstract.

In this paper we will prove a Cohen type inequality for Fourier expansions in terms of the polynomials orthogonal with respect to the generalized Jacobi weight $(1 - x)^{\alpha}(1 + x)^{\beta} \prod\nolimits_{{i = 1}}^{N} |\xi_i - x|$, where α, β > − 1, and $|\xi_i| > 1$. In particular, the norm divergence of the partial sums and Cesàro means of order δ are deduced.