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Journal of Function Spaces and Applications
Volume 8, Issue 2, Pages 181-200

Maximal operators of Fejér means of Walsh-Kaczmarz-Fourier series

1Institute of Mathematics, Faculty of Exact and Natural Sciences, Tbilisi State University, Chavchavadze str. 1, Tbilisi 0128, Georgia
2Institute of Mathematics and Computer Sciences, College of Nyíregyháza, P.O. Box 166, Nyíregyháza, H-4400, Hungary

Received 1 December 2008

Academic Editor: Maria Carro

Copyright © 2010 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The main aim of this paper is to prove that there exists a martingale fH1/2 such that the maximal Fejér operator with respect to Walsh-Kaczmarz system does not belong to the space L1/2. For the two-dimensional case, we prove that there exists a martingale fH1/2(fH1/2) such that the restricted (unrestricted) maximal operator of Fejér means of two-dimensional Walsh-Kaczmarz-Fourier series does not belong to the space weak-L1/2.