Universal functions for classes $$L^p[0,1)^2$$ L p [ 0 , 1 ) 2 , $$p\in (0,1)$$ p ∈ ( 0 , 1 ) , with respect to the double Walsh system

Abstract

In the paper it is shown that there exists a function $$U\in L^1[0,1)^2$$ , which is universal for all class $$L^{p}[0,1)^2$$ , $$p\in (0,1)$$ , by rectangles and by spheres with respect to the double Walsh system in the sense of signs of Fourier coefficients.