Polynomial Schauder basis of optimal degree with Jacobi orthogonality

In our paper we construct a polynomial Schauder basis (pα,β,n)n∈N0 of optimal degree with Jacobi orthogonality. A candidate for such a basis is given by the use of some wavelet theoretical methods, which were already successful in case of Tchebysheff and Legendre orthogonality. To prove that this sequence is in fact a Schauder basis for C[−1, 1] and as the main difficulty of the whole proof we show the uniform boundedness of its Lebesgue constants sup x∈[−1,1],n∈N0 ∥∥∥ n ∑ j=0 pα,β,j(x)pα,β,j ∥∥∥ L1ωα,β [−1,1] <∞.