On the maximal operators of Walsh-Kaczmarz-Fejér means

Abstract

The main aim of this paper is to prove that the maximal operator ${\sigma }_p^{\kappa ,\ast }f:={\sup }_{n\in \mathbf{P}}\left|{\sigma }_n^{\kappa }f\right|/{\left(n+1\right)}^{1/p-2}$ is bounded from the Hardy space to the space $L_p,$ for $0<p<1/2$.

Walsh-Kaczmarz system, Fejér means, martingale Hardy space

References in corpus (1)

• Fejér means of Vilenkin-Fourier series