On the partial sums of Vilenkin-Fourier series

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 $H_p,$ when $0<p\le 1.$

arXiv commentVilenkin system, partial sums, martingale, Hardy space, modulus of continuity, convergence. arXiv admin note: text overlap with arXiv:1410.6102, arXiv:1410.7075, arXiv:1410.7204