Some properties of the Walsh-Norlund means

Abstract

In the present paper we give a necessary and sufficient condition on monotone weights, which guaranties the N¨orlund means of Walsh-Fourier series  converge in L₁ norm and C_W norm. We also discuss the almost everywhere summability by N¨orlund means and we prove that our condition is sufficient  for almost everywhere convergence of Nörlund means for all integrable functions.