On the maximal operators of Walsh-Kaczmarz-Fejér means

The main aim of this paper is to prove that the maximal operator \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma _p^{\kappa , * } f: = \sup _{n \in P} {{\left| {\sigma _n^\kappa f} \right|} \mathord{\left/ {\vphantom {{\left| {\sigma _n^\kappa f} \right|} {\left( {n + 1} \right)^{{1 \mathord{\left/ {\vphantom {1 {p - 2}}} \right. \kern-\nulldelimiterspace} {p - 2}}} }}} \right. \kern-\nulldelimiterspace} {\left( {n + 1} \right)^{{1 \mathord{\left/ {\vphantom {1 {p - 2}}} \right. \kern-\nulldelimiterspace} {p - 2}}} }}$$\end{document} is bounded from the Hardy space Hp to the space Lp for 0 < p < 1/2.