On an analogue of Hardy's inequality for the Walsh–Fourier

According to Hardy's well-known inequality, the $l_1$-norm of a function in the Hardy space $H(T)$ consisting of $2\pi$-periodic functions serves as an upper estimate for the $l_1$-norm of the sequence of Fourier coefficients of the integral of the function. In this paper, the dyadic Hardy space $H(\mathbb R_+)$ is introduced and an analogue of this estimate is proved for the Walsh–Fourier transform.