Approximation by \(T\) means of Walsh–Fourier series
in Lebesgue spaces and Lipschitz classes

Abstract. In this paper we present and prove some new results concerning the rate of approximation of \(T\) means of functions in \(L^p(G)\) and in lip\((\alpha, p)\), for \(1\leq p\) < \(\infty\) and \(\alpha\) > \(0\). As a corollary, we obtain some new as well as known approximation inequalities.

Key words and phrases. Walsh group, Walsh system, Fejér means, \(T\) means, Lipschitz classes, approximation.