Uniform estimates for cubic oscillatory integrals
Philip Gressman
42B99oscillatory integralssymmetric spacesstationary phase
This paper establishes the optimal decay rate for scalar oscillatory integrals in $n$ variables which satisfy a nondegeneracy condition on the third derivatives. The estimates proved are stable under small linear perturbations, as encountered when computing the Fourier transform of surface-carried measures. The main idea of the proof is to construct a nonisotropic family of balls which locally capture the scales and directions in which cancellation occurs.
Indiana University Mathematics Journal
2008
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10.1512/iumj.2008.57.3403
10.1512/iumj.2008.57.3403
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Indiana Univ. Math. J. 57 (2008) 3419 - 3442
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