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

The main aim of this paper is to prove that there exists a martingale f ∈ 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 such that the restricted (unrestricted...

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Bibliographic Details
Published in:Journal of Function Spaces and Applications 2010, Vol.8 (2), p.181-200
Main Authors: Goginava, Ushangi, Nagy, Károly
Format: Article
Language:English
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Summary:The main aim of this paper is to prove that there exists a martingale f ∈ 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 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 .
ISSN:2314-8896
2314-8888
0972-6802
DOI:10.1155/2010/638327