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Estimates for an oscillatory integral operator related to restriction to space curves
| Content Provider | Semantic Scholar |
|---|---|
| Author | Bak, Jong-Guk Lee, Sanghyuk |
| Copyright Year | 2004 |
| Abstract | We consider the oscillatory integral operator defined by T λ f(x) = ∫ R e iλΦ(x,t) a(x,t)f(t)dt where λ > 1, a ∈ C∞c(R n x R) and Φ is a real-valued function in C∞(R n x R). This operator may be thought of as a variable-curve version of the adjoint of the Fourier restriction operator for space curves. Under a certain nondegeneracy condition on Φ, we obtain L p - L q estimates for T λ with a suitable bound for the operator norm ∥T λ ∥ Lp→Lq . This generalizes a result of Hormander for the plane to higher dimensions. |
| Starting Page | 1393 |
| Ending Page | 1401 |
| Page Count | 9 |
| File Format | PDF HTM / HTML |
| DOI | 10.1090/S0002-9939-03-07144-2 |
| Volume Number | 132 |
| Alternate Webpage(s) | http://www.ams.org/journals/proc/2004-132-05/S0002-9939-03-07144-2/S0002-9939-03-07144-2.pdf |
| Alternate Webpage(s) | https://doi.org/10.1090/S0002-9939-03-07144-2 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
