Almost everywhere convergence of Cesàro means of Fourier series on the group of 2-adic integers

Abstract

We prove the almost everywhere convergence of the Cesaro (C, α)-means of integrable functions σ f → f for f ∈ L 1(I), where I is the group of 2-adic integers for every α > 0. This theorem for the case of α = 1 was proved by the author [1]. For the case of the (C, 1) Fejer means there are several generalizations known with respect to some orthonormal systems. One could mention the papers [2, 9].