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 is an element of L-p such that its triangular partial sums S-2A(Delta) f of Walsh-Fourier series does not converge almost everywhere. In this paper we prove that subsequences of triangular partial sums S-nAmA(Delta) f, n(A) is an element of {1, 2, ..., m(A) - 1} on unbounded Vilenkin groups converge almost everywhere to f for each function f is an element of L-2.