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 $0<p\leq 1/2.$ 
George Tephnadze
math.AP