Divergence of the (C, 1) Means of d-dimensional Walsh-Fourier Series

In 1992, Móricz, Schipp and Wade MSW] proved for functions in L log⁺ L(I ²) (I ² is the unit square) the a.e. convergence of the double (C, 1) means of the Walsh-Fourier series _n f f as min(n ₁, n ₂) , n = (n ₁, n ₂ N ²). In the same paper, they also proved the restricted convergence of the (C, 1) means of functions in L(I ²): (2 ⁿ 1,2 ⁿ 2)f f a.e. as min (n ₁, n ₂) provided |n ₁ – n ₂| < C. The aim of this paper is to demonstrate the sharpness of these results of Móricz, Schipp and Wade with respect to both the space L log⁺ L(I ²) and the restrictedness |n ₁ – n ₂| < C.