The main result of the paper is the following: for the Walsh transform of a wavelet type system on [0, l], there is an integrable function whose Fourier expansion with respect to the transformed system is divergent almost everywhere on [0, l]. This is an extension of the result by K. S. Kazarian and A. S. Sargsian  for the bounded Ciesielski system, i.e. the Walsh transform of the Franklin system.
"The Walsh transform of wavelet type systems: divergence almost everywhere." Funct. Approx. Comment. Math. 32 57 - 66, 2004. https://doi.org/10.7169/facm/1538186625