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Let w be a generalized Jacobi weight on the interval [-1,1] and, for each function f, let Snf 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 Sn in some weighted Lp spaces. The study of the norms of the kernels Kn related to the operators Sn allows us to obtain a relation between the Fourier series with respect to different generalized Jacobi weights.

Weighted $L^p$-boundedness of Fourier series with respect to generalized Jacobi weights