  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.
