Approximation by Walsh-Kaczmarz-Fej\'er means on the Hardy space
George Tephnadze
TL;DR
This paper investigates the convergence conditions of Walsh-Kaczmarz-Fejér means in Hardy spaces for small p, providing necessary and sufficient criteria based on the modulus of continuity.
Contribution
It establishes precise convergence conditions for Walsh-Kaczmarz-Fejér means in Hardy spaces when 0<p≤1/2, advancing understanding of their behavior in these function spaces.
Findings
Convergence characterized by modulus of continuity
Necessary and sufficient conditions derived
Results applicable to Hardy spaces with 0<p≤1/2
Abstract
The main aim of this paper is to find necessary and sufficient conditions for the convergence of Walsh-Kaczmarz-Fej\'er means in the terms of the modulus of continuity on the Hardy spaces when
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