On the maximal operators of Walsh-Kaczmarz-N\"orlund means

TL;DR

This paper investigates the boundedness and almost everywhere convergence of maximal operators associated with Nörlund means of Walsh-Kaczmarz systems, providing new inequalities and convergence results in harmonic analysis.

Contribution

It establishes $(H_p, L_{p,infty})$ inequalities for Walsh-Kaczmarz-Nörlund means and proves their almost everywhere convergence, advancing understanding of these operators.

Findings

Established $(H_p, L_{p,infty})$ inequalities for maximal operators.

Proved almost everywhere convergence of Walsh-Kaczmarz-Nörlund means.

Extended harmonic analysis results to Walsh-Kaczmarz systems.

Abstract

The main aim of this paper is to investigate $\left( H_{p},L_{p,\infty }\right) $ type inequalities for maximal operators of N\"orlund means with monotone coefficients of one-dimensional Walsh-Kaczmarz system. By applying this results we conclude a.e convergence of such Walsh-Kaczmarz-N\"orlund means.