A Note on Marcinkiewicz Integrals along Submanifolds of Finite Type
We study the parametric Marcinkiewicz integrals along submanifolds of finite type with rough kernels. The kernels of our operators are allowed to be very rough both on the unit sphere and in the radial direction. Under the rather weakened size conditions on the integral kernels, the Lp bounds will b...
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2018/7052490 |
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| _version_ | 1849467527611023360 |
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| author | Daiqing Zhang |
| author_facet | Daiqing Zhang |
| author_sort | Daiqing Zhang |
| collection | DOAJ |
| description | We study the parametric Marcinkiewicz integrals along submanifolds of finite type with rough kernels. The kernels of our operators are allowed to be very rough both on the unit sphere and in the radial direction. Under the rather weakened size conditions on the integral kernels, the Lp bounds will be established for such operators. As applications, the corresponding results for parametric Marcinkiewicz integrals related to area integrals and Littlewood-Paley gλ⁎ functions are also given. |
| format | Article |
| id | doaj-art-e700f4bcf0204444912fe89902d5e4dc |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-e700f4bcf0204444912fe89902d5e4dc2025-08-20T03:26:10ZengWileyJournal of Function Spaces2314-88962314-88882018-01-01201810.1155/2018/70524907052490A Note on Marcinkiewicz Integrals along Submanifolds of Finite TypeDaiqing Zhang0College of Mathematics and Physics, Fujian University of Technology, Fuzhou, Fujian 350118, ChinaWe study the parametric Marcinkiewicz integrals along submanifolds of finite type with rough kernels. The kernels of our operators are allowed to be very rough both on the unit sphere and in the radial direction. Under the rather weakened size conditions on the integral kernels, the Lp bounds will be established for such operators. As applications, the corresponding results for parametric Marcinkiewicz integrals related to area integrals and Littlewood-Paley gλ⁎ functions are also given.http://dx.doi.org/10.1155/2018/7052490 |
| spellingShingle | Daiqing Zhang A Note on Marcinkiewicz Integrals along Submanifolds of Finite Type Journal of Function Spaces |
| title | A Note on Marcinkiewicz Integrals along Submanifolds of Finite Type |
| title_full | A Note on Marcinkiewicz Integrals along Submanifolds of Finite Type |
| title_fullStr | A Note on Marcinkiewicz Integrals along Submanifolds of Finite Type |
| title_full_unstemmed | A Note on Marcinkiewicz Integrals along Submanifolds of Finite Type |
| title_short | A Note on Marcinkiewicz Integrals along Submanifolds of Finite Type |
| title_sort | note on marcinkiewicz integrals along submanifolds of finite type |
| url | http://dx.doi.org/10.1155/2018/7052490 |
| work_keys_str_mv | AT daiqingzhang anoteonmarcinkiewiczintegralsalongsubmanifoldsoffinitetype AT daiqingzhang noteonmarcinkiewiczintegralsalongsubmanifoldsoffinitetype |