Almost everywhere convergence of varying-parameter setting Cesaro means of Fourier series on the group of 2-adic integers

Abstract

In this paper we prove that the maximal operator of Cesaro-means for one-dimensional Fourier series on the group of 2-adic integers is of weak type (L^{1}, L^{1}). Moreover, we prove the almost everywhere convergence of Cesaro means of integrable functions.