On the N\"orlund means of Vilenkin-Fourier series

TL;DR

This paper establishes optimal inequalities for weighted maximal operators of Vilenkin-Nörlund means with non-increasing coefficients, advancing understanding of their convergence properties in harmonic analysis.

Contribution

It introduces new (H_{p},L_{p})-type inequalities for Vilenkin-Nf6rlund means, demonstrating their optimality and implications for convergence theory.

Findings

Proved new inequalities for weighted maximal operators

Demonstrated the optimality of these inequalities

Applied results to convergence of Vilenkin-Nf6rlund means

Abstract

In this paper we prove and discuss some new $\left( H_{p},L_{p}\right)$-type inequalities of weighted maximal operators of Vilenkin-N\"orlund 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-N\"orlund means with non-increasing coefficients.