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 $$T_{n, \beta, \gamma}f(x)=\mathrm{p.v.} \int_{-1}^{1}f\bigl(x-\Gamma_{\theta}(t) \bigr)\frac {e^{-2\pi i \vert t \vert ^{-\beta}}}{t \vert t \...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2017-08-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13660-017-1458-0 |
| Summary: | Abstract In this paper, we study the strongly singular integrals T n , β , γ f ( x ) = p . v . ∫ − 1 1 f ( x − Γ θ ( t ) ) e − 2 π i | t | − β t | t | γ d t $$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. |
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| ISSN: | 1029-242X |