Some new restricted maximal operators of Fejér means of Walsh-Fourier series in the space $H_{1/2}$

Abstract

In this paper we derive the maximal subspace of natural numbers $\left\{n_k:k\ge 0\right\}$, such that the restricted maximal operator, defined by ${\sup }_{k\in \mathbb{N}}\left|{\sigma }_{n_k}F\right|$ 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.

arXiv admin note: substantial text overlap with arXiv:2302.12302