Subsequences of triangular partial sums of double fourier series on unbounded vilenkin groups

In 1987 Harris proved-among others-that for each 1 ≤ p < 2 there exists a two-dimensional function f ∈ L _p such that its triangular partial sums S ^△ _2A f of Walsh-Fourier series does not converge almost everywhere. In this paper we prove that subsequences of triangular partial sums S ^△ _{n M} f, n _A ∈ {1, 2, …, m _A − 1} on unbounded Vilenkin groups converge almost everywhere to f for each function ^{A A} f ∈ L ₂ .