Summation of Fourier-Walsh series (Q1820347)

In case of the Walsh orthonormal system an estimation of Lebesgue constants for triangular summability matrices is given. This is applied to show that if \((\nu_ k)\) is a convex sequence of indices such that ln \(\nu=O(\sqrt{k})\), then the \(\nu_ k\)-th partial sums \(S_{\nu_ k}(f,x)\) of the Fourier-Walsh series of function \(f\in C[0,1]\) are strongly summable to \(f(x)\) by the first arithmetic means.