Estimates for an oscillatory integral operator related to restriction to space curves
- Estimates for an oscillatory integral operator related to restriction to space curves
- Bak, JG; Lee, S
- Date Issued
- AMER MATHEMATICAL SOC
- 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.
- oscillatory integral; restriction theorem; DEGENERATE CURVES; THEOREMS
- Article Type
- PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, vol. 132, no. 5, page. 1393 - 1401, 2004-01
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