Boundedness of Oscillatory Hyper-Hilbert Transform along Curves on Sobolev Spaces
The oscillatory hyper-Hilbert transform along curves is of the following form: Hn,α,βf(x)=∫01f(x-Γ(t))eit-βt-1-αdt, where α≥0, β≥0, and Γ(t)=(tp1,tp2,…,tpn). The study on this operator is motivated by the hyper-Hilbert transform and the strongly singular integrals. The Lp bounds for Hn,α,β have be...
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| Format: | Article |
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Wiley
2014-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2014/489068 |
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| author | Jun Li Guilian Gao |
| author_facet | Jun Li Guilian Gao |
| author_sort | Jun Li |
| collection | DOAJ |
| description | The oscillatory hyper-Hilbert transform along curves is of the following form: Hn,α,βf(x)=∫01f(x-Γ(t))eit-βt-1-αdt, where α≥0, β≥0, and Γ(t)=(tp1,tp2,…,tpn). The study on this operator is motivated by the hyper-Hilbert transform and the strongly singular integrals. The Lp bounds for Hn,α,β have been given by Chen et al. (2008 and 2010). In this paper, for some α, β, and p, the boundedness of Hn,α,β on Sobolev spaces Lsp(Rn) and the boundedness of this operator from Ls2(Rn) to L2(Rn) are obtained. |
| format | Article |
| id | doaj-art-f972e4ba0c0e4e4296c7357198e2f2d8 |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-f972e4ba0c0e4e4296c7357198e2f2d82025-02-03T01:11:33ZengWileyJournal of Function Spaces2314-88962314-88882014-01-01201410.1155/2014/489068489068Boundedness of Oscillatory Hyper-Hilbert Transform along Curves on Sobolev SpacesJun Li0Guilian Gao1Department of Mathematics, Zhejiang University, Hangzhou 310027, ChinaSchool of Science, Hangzhou Dianzi University, Hangzhou 310018, ChinaThe oscillatory hyper-Hilbert transform along curves is of the following form: Hn,α,βf(x)=∫01f(x-Γ(t))eit-βt-1-αdt, where α≥0, β≥0, and Γ(t)=(tp1,tp2,…,tpn). The study on this operator is motivated by the hyper-Hilbert transform and the strongly singular integrals. The Lp bounds for Hn,α,β have been given by Chen et al. (2008 and 2010). In this paper, for some α, β, and p, the boundedness of Hn,α,β on Sobolev spaces Lsp(Rn) and the boundedness of this operator from Ls2(Rn) to L2(Rn) are obtained.http://dx.doi.org/10.1155/2014/489068 |
| spellingShingle | Jun Li Guilian Gao Boundedness of Oscillatory Hyper-Hilbert Transform along Curves on Sobolev Spaces Journal of Function Spaces |
| title | Boundedness of Oscillatory Hyper-Hilbert Transform along Curves on Sobolev Spaces |
| title_full | Boundedness of Oscillatory Hyper-Hilbert Transform along Curves on Sobolev Spaces |
| title_fullStr | Boundedness of Oscillatory Hyper-Hilbert Transform along Curves on Sobolev Spaces |
| title_full_unstemmed | Boundedness of Oscillatory Hyper-Hilbert Transform along Curves on Sobolev Spaces |
| title_short | Boundedness of Oscillatory Hyper-Hilbert Transform along Curves on Sobolev Spaces |
| title_sort | boundedness of oscillatory hyper hilbert transform along curves on sobolev spaces |
| url | http://dx.doi.org/10.1155/2014/489068 |
| work_keys_str_mv | AT junli boundednessofoscillatoryhyperhilberttransformalongcurvesonsobolevspaces AT guiliangao boundednessofoscillatoryhyperhilberttransformalongcurvesonsobolevspaces |