Almost Everywhere Convergence of Subsequence of Logarithmic Means of Walsh-fourier Series

In this paper we prove that the maximal operator of the subsequence of logarithmic means of Walsh-Fourier series is weak type (1,1). Moreover, the logarithmic means tmn (f) of the function f ∈ L converge a.e. to f as n →∞. In the literature, it is known the notion of the Riesz’s logarithmic means of a Fourier series. The n-th mean of the Fourier series of the integrable function f is defined by 1 ln n−1 ∑