Maximal operators of Fejér means of Walsh-Kaczmarz-Fourier series (Q989237)

Summary: The main aim of this paper is to prove that there exists a martingale \(f \in H_{1/2}\) such that the maximal Fejér operator with respect to Walsh- Kaczmarz system does not belong to the space \(L_{1/2 }\). For the two-dimensional case, we prove that there exists a martingale \(f \in H_{1/2}^{\square} (f \in H_{1/2})\) such that the restricted (unrestricted) maximal operator of Fejér means of two-dimensional Walsh-Kaczmarz-Fourier series does not belong to the space weak-\(L_{1/2}\).