### subsequences of Triangular Partial Sums of Double Fourier Series on Unbounded Vilenkin Groups

#### Abstract

In 1987 Harris proved-among others-that for each $1\leq p<2$ there exists a

two-dimensional function $f\in L_{p}$ such that its triangular partial sums $%

S_{2^{A}}^{\triangle }f$ of Walsh-Fourier series does not converge almost

everywhere. In this paper we prove that subsequences of triangular partial

sums $S_{n_{A}M_{A}}^{\triangle }f,n_{A}\in \left\{ 1,2,...,m_{A}-1\right\} $

on unbounded Vilenkin groups converge almost everywhere to $f$ for each

function $f\in L_{2}.$

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