Estimates for Unimodular Multipliers on Modulation Hardy Spaces
It is known that the unimodular Fourier multipliers eit|Δ|α/2, α>0, are bounded on all modulation spaces Mp,qs for 1≤p,q≤∞. We extend such boundedness to the case of all 0<p,q≤∞ and obtain its asymptotic estimate as t goes to infinity. As applications, we give the grow-up rate of the solution...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2013/982753 |
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| author | Jiecheng Chen Dashan Fan Lijing Sun Chunjie Zhang |
| author_facet | Jiecheng Chen Dashan Fan Lijing Sun Chunjie Zhang |
| author_sort | Jiecheng Chen |
| collection | DOAJ |
| description | It is known that the unimodular Fourier multipliers eit|Δ|α/2, α>0, are bounded on all modulation spaces Mp,qs for 1≤p,q≤∞. We extend such boundedness to the case of all 0<p,q≤∞ and obtain its asymptotic estimate as t goes to infinity. As applications, we give the grow-up rate of the solution for the Cauchy problems for the free Schrödinger equation with the initial data in a modulation space, as well as some mixed norm estimates. We also study the Mp1,qs→Mp2,qs boundedness for the operator eit|Δ|α/2, for the case 0<α≤2 and α≠1. Finally, we investigate the boundedness of the operator eit|Δ|α/2 for α>0 and obtain the local well-posedness for the Cauchy problem of some nonlinear partial differential equations with fundamental semigroup eit|Δ|α/2. |
| format | Article |
| id | doaj-art-39b061d2a2554641a585c95a5b183e9d |
| institution | Kabale University |
| issn | 0972-6802 1758-4965 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces and Applications |
| spelling | doaj-art-39b061d2a2554641a585c95a5b183e9d2025-02-03T00:59:30ZengWileyJournal of Function Spaces and Applications0972-68021758-49652013-01-01201310.1155/2013/982753982753Estimates for Unimodular Multipliers on Modulation Hardy SpacesJiecheng Chen0Dashan Fan1Lijing Sun2Chunjie Zhang3Department of Mathematics, Zhejiang Normal University, Jinhua 321004, ChinaDepartment of Mathematics, University of Wisconsin-Milwaukee, Milwaukee, WI 53201, USADepartment of Mathematics, University of Wisconsin-Milwaukee, Milwaukee, WI 53201, USASchool of Science, Hangzhou Dianzi University, Hangzhou 310016, ChinaIt is known that the unimodular Fourier multipliers eit|Δ|α/2, α>0, are bounded on all modulation spaces Mp,qs for 1≤p,q≤∞. We extend such boundedness to the case of all 0<p,q≤∞ and obtain its asymptotic estimate as t goes to infinity. As applications, we give the grow-up rate of the solution for the Cauchy problems for the free Schrödinger equation with the initial data in a modulation space, as well as some mixed norm estimates. We also study the Mp1,qs→Mp2,qs boundedness for the operator eit|Δ|α/2, for the case 0<α≤2 and α≠1. Finally, we investigate the boundedness of the operator eit|Δ|α/2 for α>0 and obtain the local well-posedness for the Cauchy problem of some nonlinear partial differential equations with fundamental semigroup eit|Δ|α/2.http://dx.doi.org/10.1155/2013/982753 |
| spellingShingle | Jiecheng Chen Dashan Fan Lijing Sun Chunjie Zhang Estimates for Unimodular Multipliers on Modulation Hardy Spaces Journal of Function Spaces and Applications |
| title | Estimates for Unimodular Multipliers on Modulation Hardy Spaces |
| title_full | Estimates for Unimodular Multipliers on Modulation Hardy Spaces |
| title_fullStr | Estimates for Unimodular Multipliers on Modulation Hardy Spaces |
| title_full_unstemmed | Estimates for Unimodular Multipliers on Modulation Hardy Spaces |
| title_short | Estimates for Unimodular Multipliers on Modulation Hardy Spaces |
| title_sort | estimates for unimodular multipliers on modulation hardy spaces |
| url | http://dx.doi.org/10.1155/2013/982753 |
| work_keys_str_mv | AT jiechengchen estimatesforunimodularmultipliersonmodulationhardyspaces AT dashanfan estimatesforunimodularmultipliersonmodulationhardyspaces AT lijingsun estimatesforunimodularmultipliersonmodulationhardyspaces AT chunjiezhang estimatesforunimodularmultipliersonmodulationhardyspaces |