Uniform convergence of Cesàro means of negative order of double Walsh–Fourier series Original Research Article

In this paper we prove that if f∈CW([0,1]2) and the function f is bounded partial p-variation for some p∈[1,+∞) then the double Walsh–Fourier series of the function f is uniformly (C;−α,−β) summable (α+β<1/p,α,β>0) in the sense of Pringsheim. If α+β⩾1/p then there exists a continuous function f0 of bounded partial p-variation on [0,1]2 such that the Cesàro (C;−α,−β) means σn,m−α,−β( f0;0,0) of the double Walsh–Fourier series of f0 diverge over cubes.