On the Convergence and Summability of N-Dimensional Fourier Series with Respect to the Walsh–Paley Systems in the Spaces LP ([0, 1] N ), p ∈ [1, + ∞]

Abstract

Abstract The convergence and summability of N-dimensional Walsh–Fourier series in the metrics LP ([0, 1] N ), p ∈ [1, + ∞], are studied by the negative order Césaro method. Getsadze's theorem and a generalization of Moricz' theorem are obtained as special cases.