On the convergence of Fejér means of Walsh-Fourier series in the space $H_p$

Abstract

The main aim of this paper is to find the necessary and sufficient conditions for a modulus of continuity of a martingale $F\in H_p,$ for which Fejér means convergence in $H_p$-norm, when $0<p\le 1/2.$

Walsh system, Fejér means, martingale Hardy space, modulus of continuity

References in corpus (2)

• Fejér means of Vilenkin-Fourier series
• A note on the norm convergence by Vilenkin-Fejér means