Cesàro means of double Walsh-Fourier series

We investigate approximation properties of Cesàro (C; −α, −β)-means of double Walsh-Fourier series with α, β ∈ (0, 1). As an application, we obtain a sufficient condition for the convergence of the means σ_n,m^/−α,−β (f; x, y) to f(x,y) in the L^p-metric, p ∈ [1, ∞]. We also show that this sufficient condition cannot be improved.