On the maximal operators of Walsh-Kaczmarz-Fej\'er means

TL;DR

This paper proves the boundedness of a specific maximal operator related to Walsh-Kaczmarz-Fejér means from Hardy spaces to Lebesgue spaces for certain p-values, advancing harmonic analysis theory.

Contribution

It establishes the boundedness of the maximal operator of Walsh-Kaczmarz-Fejér means from Hardy space to Lebesgue space for 0<p<1/2, a new result in harmonic analysis.

Findings

Maximal operator is bounded from H_p to L_p for 0<p<1/2.

Extends understanding of Walsh-Kaczmarz-Fejér means.

Provides new bounds in harmonic analysis.

Abstract

The main aim of this paper is to prove that the maximal operator $\sigma_{p}^{\kappa ,\ast }f:=\sup_{n\in \mathbf{P}}\left\vert \sigma_{n}^{\kappa }f\right\vert /\left( n+1\right) ^{1/p-2}$ is bounded from the Hardy space $% H_{p}$ to the space $L_{p},$ for $0<p<1/2$.