On the maximal operators of Riesz logarithmic means of Vilenkin-Fourier series

TL;DR

This paper studies the boundedness of maximal operators associated with Riesz logarithmic means of Vilenkin-Fourier series, establishing key inequalities in harmonic analysis.

Contribution

It provides new $(H_p, L_p)$ and $(H_p, L_{p, ext{infinity}})$ inequalities for these maximal operators, advancing understanding of their behavior.

Findings

Established $(H_p, L_p)$ inequalities for maximal operators.

Proved $(H_p, L_{p, ext{infinity}})$ inequalities.

Enhanced the theoretical framework of Vilenkin-Fourier analysis.

Abstract

The main aim of this paper is to investigate $\left( H_{p},L_{p}\right) $ and $\left( H_{p},L_{p,\infty }\right) $ type inequalities for maximal operators of Riesz logarithmic means of one-dimensional Vilenkin-Fourier series.