On the Nörlund means of Vilenkin-Fourier series

Abstract

In this paper we prove and discuss some new $\left(H_p,L_p\right)$-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.

arXiv admin note: text overlap with arXiv:1503.05396

References in corpus (1)

• The maximal operators of logarithmic means of one-dimensional Vilenkin-Fourier series