Almost Everywhere Convergence of Fejer Means of Two-dimensional Triangular Walsh-Fourier Series

In 1987 Harris proved ( ProcAmMath Soc 101( 4): 637- 643, 1987)- among others- that for each 1 = p < 2 there exists a two- dimensional function f. L p such that its triangular Walsh- Fourier series diverges almost everywhere. In this paper we investigate the Fejer ( or ( C, 1)) means of the triangle two variableWalsh- Fourier series of L1 functions. Namely, we prove the a. e. convergence s n f = 1 n n- 1 k= 0 Sk, n- k f. f ( n.8) for each integrable two- variable function f