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 (...
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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 |
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doaj-aafbf6b88fab4248a18c0134ba045a682020-11-24T22:25:27ZengHindawi LimitedJournal of Function Spaces and Applications0972-68022010-01-018218120010.1155/2010/638327Maximal operators of Fejér means of Walsh-Kaczmarz-Fourier seriesUshangi Goginava0Károly Nagy1Institute of Mathematics, Faculty of Exact and Natural Sciences, Tbilisi State University, Chavchavadze str. 1, Tbilisi 0128, GeorgiaInstitute of Mathematics and Computer Sciences, College of Nyíregyháza, P.O. Box 166, Nyíregyháza, H-4400, HungaryThe 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.http://dx.doi.org/10.1155/2010/638327 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Ushangi Goginava Károly Nagy |
| spellingShingle |
Ushangi Goginava Károly Nagy Maximal operators of Fejér means of Walsh-Kaczmarz-Fourier series Journal of Function Spaces and Applications |
| author_facet |
Ushangi Goginava Károly Nagy |
| author_sort |
Ushangi Goginava |
| title |
Maximal operators of Fejér means of Walsh-Kaczmarz-Fourier series |
| title_short |
Maximal operators of Fejér means of Walsh-Kaczmarz-Fourier series |
| title_full |
Maximal operators of Fejér means of Walsh-Kaczmarz-Fourier series |
| title_fullStr |
Maximal operators of Fejér means of Walsh-Kaczmarz-Fourier series |
| title_full_unstemmed |
Maximal operators of Fejér means of Walsh-Kaczmarz-Fourier series |
| title_sort |
maximal operators of fejér means of walsh-kaczmarz-fourier series |
| publisher |
Hindawi Limited |
| series |
Journal of Function Spaces and Applications |
| issn |
0972-6802 |
| publishDate |
2010-01-01 |
| description |
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. |
| url |
http://dx.doi.org/10.1155/2010/638327 |
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AT ushangigoginava maximaloperatorsoffejermeansofwalshkaczmarzfourierseries AT karolynagy maximaloperatorsoffejermeansofwalshkaczmarzfourierseries |
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