Maximal operators of Vilenkin-Nörlund means

In this paper we prove and discuss some new $\left(H_{p},weak-L_{p}\right)$ type inequalities of maximal operators of Vilenkin-Nörlund means with monotone coefficients. We also apply these results to prove a.e. convergence of such Vilenkin-Nörlund means. It is also proved that these results are the best possible in a special sense. As applications, both some well-known and new results are pointed out.

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