Sharp Hp-Lp type inequalities of weighted maximal operators of Vilenkin-Nörlund means and its applications

Abstract

We prove and discuss some new Hp-Lp type inequalities of weighted maximal operators of Vilenkin-Nörlund means with monotone coefficients. It is also proved that these inequalities are the best possible in a special sense. We also apply these results to prove strong summability for such Vilenkin-Nörlund means. As applications, both some well-known and new results are pointed out.