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In this paper we prove and discuss some new $\left(H_{p},L_{p}\right)$ typeinequalities of maximal operators of Vilenkin-N\"orlund means withnon-decreasing coefficients. We also apply these inequalities to prove strongconvergence theorems of such Vilenkin-N\"orlund means. These inequalities arethe best possible in a special sense. As applications, both some well-known andnew results are pointed out.

Some new $\left(H_{p},L_{p}\right)$ type inequalities of maximal operators of Vilenkin-N\"orlund means with non-decreasing coefficients