### Some problems arising from prediction theory and a theorem of Kolmogorov.

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Let w be a generalized Jacobi weight on the interval [-1,1] and, for each function f, let Sf denote the n-th partial sum of the Fourier series of f in the orthogonal polynomials associated to w. We prove a result about uniform boundedness of the operators S in some weighted L spaces. The study of the norms of the kernels K related to the operators S allows us to obtain a relation between the Fourier series with respect to different generalized Jacobi weights.

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