Convergence Almost Everywhere of Partial Sums and Féjer Means of Vilenkin-Fourier Series

We characterize subsequences {S-nk} of partial sums with respect to (bounded or unbounded) Vilenkin systems of f is an element of L-1(Gm) for which almost everywhere convergence holds. Moreover, we construct an explicit f is an element of L-p(G(m)), 1 <= p < infinity whose partial sums (satisfying the same conditions which guarantee almost everywhere convergence) diverges on any set of measure zero. We also prove a similar divergence result for Vilenkin-Fejer means.