On the partial sums of Vilenkin-Fourier series
George Tephnadze
TL;DR
This paper investigates the behavior of weighted maximal operators of partial sums in Vilenkin-Fourier series and applies these results to establish approximation and convergence theorems in martingale Hardy spaces for small p.
Contribution
It introduces new weighted maximal operator bounds for Vilenkin-Fourier partial sums and derives convergence results in Hardy spaces for 0<p≤1.
Findings
Boundedness of weighted maximal operators established
Strong convergence theorems proved in Hardy spaces
Approximation results for Vilenkin-Fourier series obtained
Abstract
The main aim of this paper is to investigate weighted maximal operators of partial sums of Vilenkin-Fourier series. We also use our results to prove approximation and strong convergence theorems on the martingale Hardy spaces when
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