Almost everywhere convergence of Fejer and logarithmic means of subsequences of partial sums of the Walsh-Fourier series of integrable functions

The aim of this paper is to prove some a.e. convergence results of Fejer and logarithmic means of subsequences of partial sums of Walsh Fourier series of integrable functions. We prove for lacunary sequences a that the (C, l) means of the partial sums S(a(n))f converges to f a.e. Besides, for every convex a tending to +infinity and every integrable function f the logarithmic means of the partial sums S(a(n)) f converges to f a.e. (C) 2009 Elsevier Inc. All rights reserved.