A note on the norm convergence by Vilenkin-Fej\'er means
George Tephnadze
TL;DR
This paper investigates the conditions under which Fejér means converge in Hardy spaces for small p-values, focusing on the relationship with the modulus of continuity.
Contribution
It establishes necessary and sufficient conditions for norm convergence of Fejér means in Hardy spaces $H_p$ for $0<p extless=1/2$, advancing understanding of convergence criteria.
Findings
Identifies conditions linking modulus of continuity to convergence
Provides a characterization of convergence in Hardy spaces for small p
Enhances theoretical understanding of Fejér means in harmonic analysis
Abstract
The main aim of this paper is to find necessary and sufficient conditions for the convergence of Fej\'er means in terms of the modulus of continuity on the Hardy spaces when
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