Abstract:
In the present paper we will consider the behavior of Fourier coefficients with respect to the Walsh double system after modification of functions. We prove that for any function $f(x,y)\in L^p[0,1]^2$ one can find a function $g(x,y)\in L^p[0,1]^2$ coinciding with $f(x,y)$ except a set of small measure such that the non-zero coefficients of $g(x,y)$ are monotonically decreasing over all rays in absolute value.