On the N\"orlund means of Vilenkin-Fourier series

Abstract

In this paper we prove and discuss some new $\left( H_{p},L_{p}\right)$-type inequalities of weighted maximal operators of Vilenkin-N\"orlund means with non-increasing coefficients. These results are the best possible in a special sense. As applications, both some well-known and new results are pointed out in the theory of strong convergence of Vilenkin-N\"orlund means with non-increasing coefficients.