Journal of Function Spaces

Journal of Function Spaces / 2010 / Article

Open Access

Volume 8 |Article ID 638327 | 20 pages | https://doi.org/10.1155/2010/638327

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

Academic Editor: Maria Carro
Received01 Dec 2008

Abstract

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.

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.

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