Maximal Operators of Vilenkin–Nörlund Means

By Lars-Erik Persson, George Tephnadze, Peter Wall. 2015

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In this paper we prove and discuss some new $$\left( H_{p},weak-L_{p}\right) $$Hp,weak-Lp 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.

Subfields: Applied Mathematics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/5f5e015fd312cf69b8c12f815dde374f2b60df8c