Numerical integration of Hölder continuous, absolutely convergent Fourier, Fourier cosine, and Walsh series

We introduce quasi-Monte Carlo rules for the numerical integration of functions ff defined on [0,1]s[0,1]s, s≥1s≥1, which satisfy the following properties: the Fourier, Fourier cosine or Walsh coefficients of ff are absolutely summable and ff satisfies a Hölder condition of order αα, for some 0<α≤10<α≤1. We show a convergence rate of the integration error of order max((s−1)N−1/2,sα/2N−α)max((s−1)N−1/2,sα/2N−α). The construction of the quadrature points is explicit and is based on Weil sums.