Remarks on the Unimodular Fourier Multipliers on α-Modulation Spaces
We study the boundedness properties of the Fourier multiplier operator eiμ(D) on α-modulation spaces Mp,qs,α (0≤α<1) and Besov spaces Bp,qs(Mp,qs,1). We improve the conditions for the boundedness of Fourier multipliers with compact supports and for the boundedness of eiμ(D) on Mp,qs,α. If μ is a...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2014/106267 |
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| _version_ | 1832563385543163904 |
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| author | Guoping Zhao Jiecheng Chen Weichao Guo |
| author_facet | Guoping Zhao Jiecheng Chen Weichao Guo |
| author_sort | Guoping Zhao |
| collection | DOAJ |
| description | We study the boundedness properties of the Fourier multiplier operator eiμ(D) on α-modulation spaces Mp,qs,α (0≤α<1) and Besov spaces Bp,qs(Mp,qs,1). We improve the conditions for the boundedness of Fourier multipliers with compact supports and for the boundedness of eiμ(D) on Mp,qs,α. If μ is a radial function ϕ(|ξ|) and ϕ satisfies some size condition, we obtain the sufficient and necessary conditions for the boundedness of eiϕ(|D|) between Mp1,q1s1,α and Mp2,q2s2,α. |
| format | Article |
| id | doaj-art-cfa0059a903c4451bc3f1521643a9a5a |
| 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-cfa0059a903c4451bc3f1521643a9a5a2025-02-03T01:20:26ZengWileyJournal of Function Spaces2314-88962314-88882014-01-01201410.1155/2014/106267106267Remarks on the Unimodular Fourier Multipliers on α-Modulation SpacesGuoping Zhao0Jiecheng Chen1Weichao Guo2Department of Mathematics, Zhejiang University, Hangzhou 310027, ChinaDepartment of Mathematics, Zhejiang Normal University, Jinhua 321004, ChinaDepartment of Mathematics, Xiamen University, Xiamen 361005, ChinaWe study the boundedness properties of the Fourier multiplier operator eiμ(D) on α-modulation spaces Mp,qs,α (0≤α<1) and Besov spaces Bp,qs(Mp,qs,1). We improve the conditions for the boundedness of Fourier multipliers with compact supports and for the boundedness of eiμ(D) on Mp,qs,α. If μ is a radial function ϕ(|ξ|) and ϕ satisfies some size condition, we obtain the sufficient and necessary conditions for the boundedness of eiϕ(|D|) between Mp1,q1s1,α and Mp2,q2s2,α.http://dx.doi.org/10.1155/2014/106267 |
| spellingShingle | Guoping Zhao Jiecheng Chen Weichao Guo Remarks on the Unimodular Fourier Multipliers on α-Modulation Spaces Journal of Function Spaces |
| title | Remarks on the Unimodular Fourier Multipliers on α-Modulation Spaces |
| title_full | Remarks on the Unimodular Fourier Multipliers on α-Modulation Spaces |
| title_fullStr | Remarks on the Unimodular Fourier Multipliers on α-Modulation Spaces |
| title_full_unstemmed | Remarks on the Unimodular Fourier Multipliers on α-Modulation Spaces |
| title_short | Remarks on the Unimodular Fourier Multipliers on α-Modulation Spaces |
| title_sort | remarks on the unimodular fourier multipliers on α modulation spaces |
| url | http://dx.doi.org/10.1155/2014/106267 |
| work_keys_str_mv | AT guopingzhao remarksontheunimodularfouriermultipliersonamodulationspaces AT jiechengchen remarksontheunimodularfouriermultipliersonamodulationspaces AT weichaoguo remarksontheunimodularfouriermultipliersonamodulationspaces |