On the divergence of Nörlund logarithmic means of Walsh-Fourier series

It is well known in the literature that the logarithmic means 1-k = 1n - 1 S-k f k of Walsh or trigonometric Fourier series converge a.e. to the function for each integrable function on the unit interval. This is not the case if we take the partial sums. In this paper we prove that the behavior of the so-called Nörlund logarithmic means 1 logn-k = 1 n - 1 S-k (f) n - k is closer to the properties of partial sums in this point of view.