Uniform estimates for cubic oscillatory integrals

Details Uniform estimates for cubic oscillatory integrals Uniform estimates for cubic oscillatory integrals

2007-07-17

arxiv.org/abs/0707.2557v2

Mathematics

Classical Analysis and ODEs

22 pages; v2 added references

Scientific paper

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.

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