Martingale Morrey-Campanato Spaces and Fractional Integrals
We introduce Morrey-Campanato spaces of martingales and give their basic properties. Our definition of martingale Morrey-Campanato spaces is different from martingale Lipschitz spaces introduced by Weisz, while Campanato spaces contain Lipschitz spaces as special cases. We also give the relation bet...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2012/673929 |
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| author | Eiichi Nakai Gaku Sadasue |
| author_facet | Eiichi Nakai Gaku Sadasue |
| author_sort | Eiichi Nakai |
| collection | DOAJ |
| description | We introduce Morrey-Campanato spaces of martingales and give their basic properties. Our definition of martingale Morrey-Campanato spaces is different from martingale Lipschitz spaces introduced by Weisz, while Campanato spaces contain Lipschitz spaces as special cases. We also give the relation between these definitions. Moreover, we establish the boundedness of fractional integrals as martingale transforms on these spaces. To do this we show the boundedness of the maximal function on martingale Morrey-Campanato spaces. |
| format | Article |
| id | doaj-art-bfedc52958754cee855e21ac4073d1fc |
| institution | Kabale University |
| issn | 0972-6802 1758-4965 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces and Applications |
| spelling | doaj-art-bfedc52958754cee855e21ac4073d1fc2025-02-03T01:03:38ZengWileyJournal of Function Spaces and Applications0972-68021758-49652012-01-01201210.1155/2012/673929673929Martingale Morrey-Campanato Spaces and Fractional IntegralsEiichi Nakai0Gaku Sadasue1Department of Mathematics, Ibaraki University, Mito, Ibaraki 310-8512, JapanDepartment of Mathematics, Osaka Kyoiku University, Kashiwara, Osaka 582-8582, JapanWe introduce Morrey-Campanato spaces of martingales and give their basic properties. Our definition of martingale Morrey-Campanato spaces is different from martingale Lipschitz spaces introduced by Weisz, while Campanato spaces contain Lipschitz spaces as special cases. We also give the relation between these definitions. Moreover, we establish the boundedness of fractional integrals as martingale transforms on these spaces. To do this we show the boundedness of the maximal function on martingale Morrey-Campanato spaces.http://dx.doi.org/10.1155/2012/673929 |
| spellingShingle | Eiichi Nakai Gaku Sadasue Martingale Morrey-Campanato Spaces and Fractional Integrals Journal of Function Spaces and Applications |
| title | Martingale Morrey-Campanato Spaces and Fractional Integrals |
| title_full | Martingale Morrey-Campanato Spaces and Fractional Integrals |
| title_fullStr | Martingale Morrey-Campanato Spaces and Fractional Integrals |
| title_full_unstemmed | Martingale Morrey-Campanato Spaces and Fractional Integrals |
| title_short | Martingale Morrey-Campanato Spaces and Fractional Integrals |
| title_sort | martingale morrey campanato spaces and fractional integrals |
| url | http://dx.doi.org/10.1155/2012/673929 |
| work_keys_str_mv | AT eiichinakai martingalemorreycampanatospacesandfractionalintegrals AT gakusadasue martingalemorreycampanatospacesandfractionalintegrals |