On the $\left(C,\alpha\right) $-means with respect to the Walsh system

TL;DR

This paper establishes strong convergence theorems for Cesàro means of order lpha in Hardy spaces associated with the Walsh system, advancing understanding of convergence behaviors in harmonic analysis.

Contribution

It proves new strong convergence results for lpha-Cesro means on Hardy spaces related to the Walsh system, extending prior convergence theorems.

Findings

Strong convergence theorems for Cesro means lpha in Hardy spaces.

Convergence results hold for 0 < lpha < 1.

Advances the theory of Walsh system and harmonic analysis.

Abstract

As main result we prove strong convergence theorems for Ces\'aro means $% \left(C,\alpha \right) $ on the Hardy spaces $H_{1/\left(1+\alpha \right) } $% , where $0<\alpha <1.$