Approximation by Nörlund means of Walsh-Fourier series

We study the rate of approximation by Nörlund means for Walsh-Fourier series of a function in L^p and, in particular, in Lip(α, p) over the unit interval 0, 1), where α > 0 and 1 p ∞. In case p = ∞, by L^p we mean C_W, the collection of the uniformly W-continuous functions over 0, 1). As special cases, we obtain the earlier results by Yano, Jastrebova, and Skvorcov on the rate of approximation by Cesàro means. Our basic observation is that the Nörlund kernel is quasi-positive, under fairly general assumptions. This is a consequence of a Sidon type inequality. At the end, we raise two problems.