On the divergence of double Fourier-Walsh and Fourier-Walsh-Kaczmarz series of continuous functions (Q2043677)

In [Acta Sci. Math. 86, No. 1--2, 287--302 (2020; Zbl 1463.42065)] the author proved the existence of a continuous bivariate function on \( [0,1]^2 \) with certain smoothness, whose double Fourier series with respect to the orthonormal Walsh-Paley system diverges by rectangles on a set of positive measure.\par Here this result is extended (under the same suppositions on the smoothness) to the cases of orthonormal Walsh and Walsh-Kaczmarcz systems.