Strongly singular integrals along curves on α-modulation spaces
Abstract In this paper, we study the strongly singular integrals T n , β , γ f ( x ) = p . v . ∫ − 1 1 f ( x − Γ θ ( t ) ) e − 2 π i | t | − β t | t | γ d t $$T_{n, \beta, \gamma}f(x)=\mathrm{p.v.} \int_{-1}^{1}f\bigl(x-\Gamma_{\theta}(t) \bigr)\frac {e^{-2\pi i \vert t \vert ^{-\beta}}}{t \vert t \...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2017-08-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13660-017-1458-0 |
| _version_ | 1819207355530739712 |
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| author | Xiaomei Wu Xiao Yu |
| author_facet | Xiaomei Wu Xiao Yu |
| author_sort | Xiaomei Wu |
| collection | DOAJ |
| description | Abstract In this paper, we study the strongly singular integrals T n , β , γ f ( x ) = p . v . ∫ − 1 1 f ( x − Γ θ ( t ) ) e − 2 π i | t | − β t | t | γ d t $$T_{n, \beta, \gamma}f(x)=\mathrm{p.v.} \int_{-1}^{1}f\bigl(x-\Gamma_{\theta}(t) \bigr)\frac {e^{-2\pi i \vert t \vert ^{-\beta}}}{t \vert t \vert ^{\gamma}}\,dt $$ along homogeneous curves Γ θ ( t ) $\Gamma_{\theta}(t)$ . We prove that T n , β , γ $T_{n, \beta, \gamma}$ is bounded on the α-modulation spaces, including the inhomogeneous Besov spaces and the classical modulation spaces. |
| first_indexed | 2024-12-23T05:22:11Z |
| format | Article |
| id | doaj.art-47defc99b5da4e9cb3fe2d50220328e1 |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-12-23T05:22:11Z |
| publishDate | 2017-08-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-47defc99b5da4e9cb3fe2d50220328e12022-12-21T17:58:40ZengSpringerOpenJournal of Inequalities and Applications1029-242X2017-08-012017111310.1186/s13660-017-1458-0Strongly singular integrals along curves on α-modulation spacesXiaomei Wu0Xiao Yu1Xingzhi College, Zhejiang Normal UniversityDepartment of Mathematics, Shangrao Normal UniversityAbstract In this paper, we study the strongly singular integrals T n , β , γ f ( x ) = p . v . ∫ − 1 1 f ( x − Γ θ ( t ) ) e − 2 π i | t | − β t | t | γ d t $$T_{n, \beta, \gamma}f(x)=\mathrm{p.v.} \int_{-1}^{1}f\bigl(x-\Gamma_{\theta}(t) \bigr)\frac {e^{-2\pi i \vert t \vert ^{-\beta}}}{t \vert t \vert ^{\gamma}}\,dt $$ along homogeneous curves Γ θ ( t ) $\Gamma_{\theta}(t)$ . We prove that T n , β , γ $T_{n, \beta, \gamma}$ is bounded on the α-modulation spaces, including the inhomogeneous Besov spaces and the classical modulation spaces.http://link.springer.com/article/10.1186/s13660-017-1458-0α-modulation spacesstrongly singular integralsBesov spaceshomogeneous curves |
| spellingShingle | Xiaomei Wu Xiao Yu Strongly singular integrals along curves on α-modulation spaces Journal of Inequalities and Applications α-modulation spaces strongly singular integrals Besov spaces homogeneous curves |
| title | Strongly singular integrals along curves on α-modulation spaces |
| title_full | Strongly singular integrals along curves on α-modulation spaces |
| title_fullStr | Strongly singular integrals along curves on α-modulation spaces |
| title_full_unstemmed | Strongly singular integrals along curves on α-modulation spaces |
| title_short | Strongly singular integrals along curves on α-modulation spaces |
| title_sort | strongly singular integrals along curves on α modulation spaces |
| topic | α-modulation spaces strongly singular integrals Besov spaces homogeneous curves |
| url | http://link.springer.com/article/10.1186/s13660-017-1458-0 |
| work_keys_str_mv | AT xiaomeiwu stronglysingularintegralsalongcurvesonamodulationspaces AT xiaoyu stronglysingularintegralsalongcurvesonamodulationspaces |