Convergence of a Subsequence of Triangular Partial Sums of Double Walsh-Fourier Series

摘要

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 triangularWalsh-Fourier series does not converge almost everywhere. In this paper we prove that the set of the functions from the space L-p(I-2) (1 <= p < 2) with subsequence of triangular partial means S-2A(Delta)(f) of the doubleWalsh-Fourier series convergent in measure on I-2 is of first Baire category in L-p(I-2). We also prove that for each function f is an element of L-2(I-2) a.e. convergence S-a(n)(Delta)(f) -> f holds, where a(n) is a lacunary sequence of positive integers.