Almost everywhere convergence of Fejér 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,1) means of the partial sums S"a"("n")f converges to f a.e. Besides, for every convex a tending to +~ and every integrable function f the logarithmic means of the partial sums S"a"("n")f converges to f a.e.