Approximation by Θ-Means of Walsh–Fourier Series

We discuss the behaviour of the Θ-means of Walsh series of a function in L p (1 ≤ p ≤ ∞). We investigate the rate of the approximation by this means, in particular, in Lip(α, p), where α > 0 and 1 ≤ p ≤ ∞. In case p = ∞ by L p we mean C, the class of the continuous functions.