Almost everywhere divergence of two-dimensional Walsh-Fourier series

C. Fefferman [1], [2], [3] has shown that the two-dimensional Fourier series of an f ∈ L^p , p < 2 , may diverge a.e. when summed over expanding circles, but converges a.e. when summed over expanding polygonal arcs. We show this dichotomy does not prevail for two-dimensional Walsh-Fourier series.

To prove our results we prove the unboundedness of a large class of multiplier operators on L^p , p ≠ 2 .