Almost everywhere summability of multiple Walsh–Fourier series

We prove that for the N-dimensional Walsh–Fourier series the maximal operator of the Marcinkiewicz means is of weak type (1, 1). Moreover, the Marcinkiewicz means σnf of the function f ∈ L1 converge a.e. to f as n→∞.  2003 Elsevier Inc. All rights reserved.