Strong convergence theorems of Walsh-Fej\'er means

TL;DR

This paper proves that Fejér means of Walsh-Fourier series are uniformly bounded operators on Hardy spaces for certain p-values, advancing the understanding of convergence in harmonic analysis.

Contribution

It establishes strong convergence theorems for Walsh-Fejér means on Hardy spaces, extending previous results to the range 0<p≤1/2.

Findings

Fejér means are uniformly bounded on H_p spaces for 0<p≤1/2

The results improve understanding of Walsh-Fourier series convergence

Provides new bounds for Walsh-Fejér operators

Abstract

As main result we prove that Fej\'er means of Walsh-Fourier series are uniformly bounded operators from $\ H_{p}$ to $H_{p}$ $\left( 0<p\leq 1/2\right) .