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

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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.