Some weak type inequalities and almost everywhere convergence of Vilenkin–Nörlund means

Abstract

We prove and discuss some new weak type (1,1 ) inequalities of maximal operators of Vilenkin–Nörlund means generated by monotone coefficients. Moreover, we use these results to prove a.e. convergence of such Vilenkin–Nörlund means. As applications, both some well-known and new inequalities are pointed out.