OnW1,p-convergence of Fourier–Sobolev expansions

Abstract

Keywords:Sobolev orthogonal polynomials Weighted Sobolev spaces Fourier expansions Sobolev-Fourier expansions a b s t r a c t Let {q n } n≥0 be the sequence of polynomials orthonormal with respect to the Sobolev inner product ⟨f , g⟩ S := 1]) and w 1 is a weight of Kufner-Opic type. We study necessary and/or sufficient conditions for the convergence in the W 1,p ([−1, 1], (w 0 , w 1 )) norm of the Fourier expansion in terms of {q n } n≥0 , with 1 < p < ∞.