Maximal operators of Vilenkin-N\"orlund means

In this paper we prove and discuss some new $(H_p,weak-L_p)$ type inequalities of maximal operators of Vilenkin-N"orlund means with monotone coefficients. We also apply these results to prove a.e. convergence of such Vilenkin-N"orlund means. It is also proved that these results are the best possible in a special sense. As applications, both some well-known and new results are pointed out.