Convergence of Ces'{a}ro means with varying parameters of Walsh-Fourier series

摘要

In 2007 Akhobadze [1] (see also [2]) introduced the notion of Ces`{a}ro means of Fourier series with variable parameters. In the present paper we prove the almost everywhere convergence of the the Ces`{a}ro $ (C , lpha_{n})$ means of integrable functions$sigma _{n}^{lpha_{n}} f o f$, where $mathbb{N}_{lpha, K}i no infty$ for $ f in L^{1}(I) $, where $I$ is the Walsh group for every sequence $lpha = (lpha_n)$,$ 0 lpha_{n} 1 $. This theorem for constant sequences $lpha$ that is, $ lpha equiv lpha_1 $ was proved by Fine [3].