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Estimates for an oscillatory integral operator related to restriction to space curves
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- Title
- Estimates for an oscillatory integral operator related to restriction to space curves

- Date Issued
- 2004-01

- Publisher
- AMER MATHEMATICAL SOC

- Abstract
- We consider the oscillatory integral operator de fined by T(lambda)f(x) = integral(R)e(ilambdaphi(x,t))a(x, t)f(t)dt where lambda > 1, a 2 C-c(infinity) (R-n x R) and phi is a real-valued function in C-infinity(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 phi, we obtain L-p - L-q estimates for T-lambda with a suitable bound for the operator norm parallel toT(lambda)parallel to(Lp)-->(Lq). This generalizes a result of Hormander for the plane to higher dimensions.

- Keywords
- oscillatory integral; restriction theorem; DEGENERATE CURVES; THEOREMS

- ISSN
- 0002-9939

- Article Type
- Article

- Citation
- PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, vol. 132, no. 5, page. 1393 - 1401, 2004-01

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- 박종국BAK, JONG GUK
- Dept of Mathematics

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