Integrability of the sum of absolute values of blocks of the Fourier–Walsh series for functions of bounded variation

We establish necessary and sufficient conditions on a sequence that splits the Fourier–Walsh series into blocks under which the series consisting of the absolute values of such blocks of the Fourier–Walsh series of any function of bounded variation converges to an integrable function. We also obtain estimates for the $L$-norms of the Walsh–Dirichlet kernels and their differences.