On the convergence of Fej\'er means of Walsh-Fourier series in the space $H_p$

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 Fej'er means convergence in $H_p$-norm, when $0<p\le 1\mathrm{/}2.$