## On Fourier coefficients with respect to the Walsh double system.(English)Zbl 1301.42011

Summary: 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 $$f(x,y)$$ 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.

### MSC:

 42A65 Completeness of sets of functions in one variable harmonic analysis 42A20 Convergence and absolute convergence of Fourier and trigonometric series