Uniform convergence of Cesàro means of negative order of double trigonometric Fourier series

In this paper we prove that if f ∈ C([-π, π]²) and the function f is bounded partial p-variation for some p ∈ [1,+ ∞), then the double trigonometric Fourier series of a 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 f ₀ of bounded partial p-variation on [-π, π]² such that the Cesàro (C;-α,-β) means σ _n,m ^-α,-β (f ₀;0,0) of the double trigonometric Fourier series of f ₀ diverge over cubes.