Almost everywhere convergence of Fejér and logarithmic means of subsequences of partial sums of the Walsh–Fourier series of integrable functions Original Research Article

The aim of this paper is to prove some a.e. convergence results of Fejér and logarithmic means of subsequences of partial sums of Walsh–Fourier series of integrable functions. We prove for lacunary sequences aa that the (C,1)(C,1) means of the partial sums Sa(n)fSa(n)f converges to ff a.e. Besides, for every convex aa tending to +∞+∞ and every integrable function ff the logarithmic means of the partial sums Sa(n)fSa(n)f converges to ff a.e.