On the Uniform Convergence of Spherical Partial Sums of Fourier Series by the Double Walsh System

In this paper, we construct a two-variable integrable function U whose Fourier coefficients by the double Walsh system are positive on the spectrum and arranged in decreasing order in all directions. For each almost every where finite measurable function f(x, y),(x, y)is an element of[0,1)(2),and for any delta>0 it is possible to find a bounded function g(x, y)such that |{(x, y)is an element of[0,1)(2):g(x, y)not equal f(x, y)}<= delta, and |c(k,s)(g)|=c(k,s)(U)on the spectrum of the function g, and its spherical partial sums of the Fourier series by the double Walsh system converge uniformly on[0,1)(2)