On the approximation properties of Cesàro means of negative order of Walsh-Fourier series
Some approximation properties of Cesàro \((C,-\alpha)\) means with \(0<\alpha<1\) of Walsh-Fourier series are given. A sufficient condition for the convergence of the means \(\sigma_n^{-\alpha} f\) to \(f\) in \(L_p\) norm \((1\leq p \leq \infty)\) is obtained. It is also shown that this condition cannot be improved in the case \(p=1\).
scientific article; zbMATH DE number 1750337
scientific article