In this paper we derive the restricted weighted maximal operator, defined by ${ \sup }_{ k\in \mathbb{ N}}\left(\left\vert \sigma _{ k}F\right\vert/A^2_k\right)$ of Fej\'er means of Walsh-Fourier series and prove that the it is bounded from the martingale Hardy space $H_{ 1/2}(G)$ to the Lebesgue space $L_{ 1/2}(G).$ The sharpness of this result is also proved. As a consequence we obtain some new and and well-know results.
Categories: math.CA