University of Nyíregyháza and Ivane Javakhishvili Tbilisi State University
Abstract: In this paper we prove and discuss some new $( H_{p},L_{p})$-type inequalities of weighted maximal operators of Vilenkin-Nörlund 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-Nörlund means with non-increasing coefficients.
Keywords: Vilenkin systems, Vilenkin groups, Nörlund means, martingale Hardy spaces, maximal operator, Vilenkin-Fourier series, strong convergence, inequalities
Classification (MSC2000): 42C10; 42B25
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