Abstract
We prove and discuss some new (H p ,L p )-type inequalities of weighted maximal operators of Vilenkin-Norlund means with non-increasing coefficients {q k : k ⩾ 0}. These results are the best possible in a special sense. As applications, some well-known as well as new results are pointed out in the theory of strong convergence of such Vilenkin-Norlund means. To fulfil our main aims we also prove some new estimates of independent interest for the kernels of these summability results. In the special cases of general Norlund means t n with non-increasing coefficients analogous results can be obtained for Fejer and Cesaro means by choosing the generating sequence {q k : k ⩾ 0} in an appropriate way.
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