Some new restricted maximal operators of Fejér means of Walsh–Fourier series

Abstract

In this paper, we derive the maximal subspace of natural numbers { <i>n_k</i> : <i>k</i> &#8805; 0 }, such that the restricted maximal operator, defined by sup_{<i>k</i>&#8712;&#8469;} | &sigma;<i>_{n_k}F</i> | on this subspace of Fejér means of Walsh–Fourier series is bounded from the martingale Hardy space <i>H</i>_1/2 to the Lebesgue space <i>L</i>_1/2. The sharpness of this result is also proved.