Abstract
In this paper, we derive the maximal subspace of natural numbers left{ n_{k}:kge 0right} , such that the restricted maximal operator, defined by {sup }_{kin {mathbb {N}}}left| sigma _{n_{k}}Fright| on this subspace of Fejér means of Walsh–Fourier series is bounded from the martingale Hardy space H_{1/2} to the Lebesgue space L_{1/2}. The sharpness of this result is also proved.
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