ON FOURIER COEFFICIENTS WITH RESPECT TO THE WALSH DOUBLE SYSTEM

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 $g\in L^{p}[0,1]^{2}$ coinciding with $f(x,y)$ on a small measure such that the non-zero coefficients of $g(x,y)$ are monotonically decreasing over all rays by absolute values.