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∈ H1/2 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 f∈H1/2□(f∈H1/2) such that the restricted (...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2010-01-01
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| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2010/638327 |
| Summary: | The main aim of this paper is to prove that there exists a martingale f∈ H1/2 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 f∈H1/2□(f∈H1/2) 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. |
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| ISSN: | 0972-6802 |